When the diode is forward biased, it is found that beyond forward voltage V = V_k, called knee voltage, the conductivity is very high. At this value of battery biasing for p-n junction,the potential barrier is overcome and the current increases rapidly with increase in forward voltage. When the diode is reverse biased, the reverse bias voltage produces a very small current about a few microamperes which almost remains constant with bias. This small current is reverse saturation current.
(i) In which of the following figures, the p-n diode is forward biased.

(ii) Based on the V-I characteristics of the diode, we can classify diode as

(iii) The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is

(iv) In the case of forward biasing of a p-n junction diode, which one of the following figures correctly depicts the direction of conventional current (indicated by an arrow mark)?

(v) If an ideal junction diode is connected as shown, then the value of the current I is

Rectifier is a device which is used for converting alternating current or voltage into direct current or voltage. Its working is based on the fact that the resistance of p-n junction becomes low when forward biased and becomes high when reverse biased. A half-wave rectifier uses only a single diode while a full wave rectifier uses two diodes as shown in figures (a) and (b) .

(i) If the rms value of sinusoidal input to a full wave rectifier is \(\frac{V_{0}}{\sqrt{2}}\) then the rms value of the rectifier's output is

(ii) In the-diagram, the input ac is actoss the terminals A and C. The output across Band D is

(iii) A bridge rectifier is shown in figure. Alternating input is given across A and C. If output is taken across BD, then it is

(iv) A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit. The current (I) in the resistor(R) can be shown by

(v) With an ac input from 50 Hz power line, the ripple frequency is

From Bohr's atomic model, we know that the electrons have well defined energy levels in an isolated atom. But due to interatomic interactions in a crystal, the electrons of the outer shells are forced to have energies different from those in isolated atoms. Each energy level splits into a number of energy levels forming a continuous band.The gap between top of valence band and bottom of the conduction band in which no allowed energy levels for electrons can exist is called energy gap.

(i) In an insulator energy band gap is

(ii) In a semiconductor, separation between conduction and valence band is of the order of

(iii) Based on the band theory of conductors, insulators and semiconductors, the forbidden gap is smallest in

(iv) Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?

(v) Solids having highest energy level partially filled with electrons are

Light emitting diode is a photoelectric device which converts electrical energy into light energy. It is a heavily doped p-n junction diode which under forward biased emits spontaneous radiation. The general shape of the J- V characteristics of an LED is similar to that of a normal p-n junction diode, as shown. The barrier potentials are much higher and slightly different for each colour.

(i) The J- V characteristic of an LED is

(ii) The schematic symbol of light emitting diode is (LED)

(iii) An LED is constructed from a p-n junction based on a certain Ga-As-P semiconducting material whose energy gap is 1.9 eV. Identify the colour of the emitted light.

(iv) Which one of the following statement is not correct in the case of light emitting diodes?

(v) The energy of radiation emitted by LED is

A photodiode is an optoelectronic device in which current carriers are generated by photons through photoexcitation i.e., photo conduction by light. It is a p-n junction fabricated from a photosensitive semiconductor and provided with a transparent window so as allow light to fall on its function. A photodiode can turn its current ON and OFF in nanoseconds. So, it can be used as a fastest photo-detector.

(i) A p-n photo diode is fabricated from a semiconductor with a band gap of 2.5 ev' It can detect a signal of wavelength

(ii) Three photo diodes D₁ D₂ and D₃ are made of semiconductors having band gap of 2.5 eV, 2 eV and 3 eV, respectively. Which one will be able to detect light of wavelength 6000 \(\dot A\) ?

(iii) Photodiode is a device

(iv) To detect light of wavelength 500 nrn, the photodiode must be fabricated from a semiconductor of minimum bandwidth of

(v) Photo diode can be used as a photo detector to detect

In the year 1939, German scientist Otto Hahn and Strassmann discovered that when an uranium isotope was bombarded with a neutron, it breaks into two intermediate mass fragments. It was observed that, the sum of the masses of new fragments formed were less than the mass of the original nuclei. This difference in the mass appeared as the energy released in the process. Thus, the phenomenon of splitting of a heavy nucleus (usually A> 230) into two or more lighter nuclei by the bombardment of proton, neutron, a-particle, etc with liberation of energy is called nuclear fission.
\({ }_{92} \mathrm{U}^{235}+{ }_{0} n^{1} \rightarrow \quad{ }_{92} \mathrm{U}^{236} \rightarrow{ }_{56} \mathrm{Ba}^{144}+{ }_{36} \mathrm{Kr}^{89}+3{ }_{0} n^{1}+Q\)
Unstable nucleus
(i) Nuclear fission can be explained on the basis of

(ii) For sustaining the nuclear fission chain reaction in a sample (of small size) \({ }_{92}^{235} \mathrm{U}\), it is desirable to slow down fast neutrons by

(iii) Which of the following is/are fission reaction(s)?
\(\text {(I) }{ }_{0}^{1} n+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{92}^{236} \mathrm{U} \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{99} \mathrm{Nb}+4_{0}^{1} n\)
\(\text {(II) }{ }_{0}^{1} n+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{54}^{1.40} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+2{ }_{0}^{1} n\)
\((\mathrm{III}){ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} n\)

(iv) On an average, the number of neutrons and the energy of a neutron released per fission of a uranium atom are respectively

(v) In any fission process, ratio of mass of daughter nucleus to mass of parent nucleus is

The nucleus was first discovered in 1911 by Lord Rutherford and his associates by experiments on scattering of a-particles by atoms. He found that the scattering results could be explained, if atoms consist of a small, central, massive and positive core surrounded by orbiting electrons. The experimental results indicated that the size of the nucleus is of the order of 10^-14m and is thus 10000 times smaller than the size of atom.
(i) Ratio of mass of nucleus with mass of atom is approximately

(ii) Masses of nuclei of hydrogen, deuterium and tritium are in ratio

(iii) Nuclides with same neutron number but different atomic number are

(iv) If R is the radius and A is the mass number, then log R versus log A graph will be

(v) The ratio of the nuclear radii of the gold isotope \({ }_{79}^{197} \mathrm{Au}\) and silver isotope \({ }_{47}^{107} \mathrm{Au}\) is

A heavy nucleus breaks into comparatively lighter nuclei which are more stable compared to the original heavy nucleus. When a heavy nucleus like uranium is bombarded by slow moving neutrons, it splits into two parts releasing large amount of energy. The typical fission reaction of \({ }_{92} \mathrm{U}^{235}\).
\({ }_{92} \mathrm{U}^{235}+{ }_{0} n^{1} \rightarrow{ }_{56} \mathrm{Ba}^{141}+{ }_{36} \mathrm{Kr}^{92}+3{ }_{0} n^{1}+200 \mathrm{MeV}\)
The fission of ₉₂U²³⁵approximately released 200 MeV of energy.
(i) If 200 MeV energy is released in the fission of a single nucleus of \({ }_{92}^{235} \mathrm{U}\),the fissions which are required to produce a power of 1kW is

(ii) The release in energy in nuclear fission is consistent with the fact that uranium has

(iii) When ₉₂U²³⁵undergoes fission, about 0.1% of the original mass is converted into energy. The energy released when 1 kg of ₉₂U²³⁵undergoes fission is

(iv) A nuclear fission is said to be critical when multiplication factor or K

(v) Einstein's mass-energy conversion relation E = mc² is illustrated by

Neutrons and protons are identical particle in the sense that their masses are nearly the same and the force, called nuclear force, does into distinguish them. Nuclear force is the strongest force. Stability of nucleus is determined by the neutron proton ratio or mass defect or packing fraction. Shape of nucleus is calculated by quadrupole moment and spin of nucleus depends on even or odd mass number. Volume of nucleus depends on the mass number. Whole mass of the atom (nearly 99%) is centred at the nucleus.
(i) The correct statements about the nuclear force is/are

(ii) The range of nuclear force is the order of

(iii) A force between two protons is same as the force between proton and neutron. The nature of the force is

(iv) Two protons are kept at a separation of 40 \(\dot A\). Fn is the nuclear force and F_e is the electrostatic force between them. Then

(v) All the nucleons in an atom are held by

The density of nuclear matter is the ratio of the mass of a nucleus to its volume. As the volume of a nucleus is directly proportional to its mass number A, so the density of nuclear matter is independent of the size of the nucleus. Thus, the nuclear matter behaves like a liquid of constant density. Different nuclei are like drops of this liquid, of different sizes but of same density.
Let A be the mass number and R be the radius of a nucleus. If m is the average mass of a nucleon, then
Mass of nucleus = mA
\(\text { Volume of nucleus }=\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi\left(R_{0} A^{1 / 3}\right)^{3}=\frac{4}{3} \pi R_{0}^{3} A\)
\(\text { Nuclear density, } \rho_{\mathrm{nu}}=\frac{\text { Mass of nucleus }}{\text { Volume of nucleus }} \text { or } \rho_{\mathrm{nu}}=\frac{m A}{\frac{4}{3} \pi R_{0}^{3} A}=\frac{3 m}{4 \pi R_{0}^{3}}\)
Clearly, nuclear density is independent of mass number A or the size of the nucleus. The nuclear mass density is of the order 10¹⁷ kg m^-3. This density is very large as compared to the density of ordinary matter, say water, for which p = 1.0 x 10³ kg m^-3.
(i) The nuclear radius of \({ }_{8}^{16} \mathrm{O}\) is 3 X 10^-15 m. The density of nuclear matter is

(ii) What is the density of hydrogen nucleus in SI units? Given R_o = 1.1 fermi and m_p = 1.007825 amu

(iii) Density of a nucleus is

(iv) The nuclear mass of \({ }_{26}^{56} \mathrm{Fe}\) is 55.85 amu. The its nuclear density is

(v) If the nucleus of \({ }_{13}^{27} \mathrm{Al}\) has a nuclear radius of about 3.6 fm, then \({ }_{52}^{125} \mathrm{Te}\) would have its radius approximately as

Niels Bohr introduced the atomic Hydrogen model in 1913. He described it as a positively charged nucleus, comprised of protons and neutrons, surrounded by a negatively charged electron cloud. In the model, electrons orbit the nucleus in atomic shells. The atom is held together by electrostatic forces between the positive nucleus and negative surroundings.

Bohr correctly proposed that the energy and radii of the orbits of electrons in atoms are quantized, with energy for transitions between orbits given by
\(\Delta E=h v=E_{i}-E_{f}\) Where \(\Delta E\) is the change in energy between the initial and final orbits and hv is the energy of an absorbed or emitted photon.
(i) In the Bohr model of the hydrogen atom, discrete radii and energy states result when an electron circles the atom in an integer number of

(ii) The angular speed of the electron in the n^th orbit of Bohr's hydrogen atom is

(iii) When electron jumps from n = 4 level to n = 1 level, the angular momentum of electron changes by

(iv) The lowest Bohr orbit in hydrogen atom has

(v) Which of the following postulates of the Bohr modelled to the quantization of energy of the hydrogen atom?

In 1911, Rutherford, along with his assistants, H. Geiger and E. Marsden, performed the alpha particle scattering experiment. H. Geiger and E. Marsden took radioactive source \(\left(\begin{array}{c} 214 \\ 83 \end{array} \mathrm{Bi}\right)\) for a-particles. A collimated beam of a-particles of energy 5.5 MeV was allowed to fall on 2.1 x 10^-7 m thick gold foil. The a-particles were observed through a rotatable detector consisting of a Zinc sulphide screen and microscope. It was found that a-particles got scattered. These scattered a-particles produced scintillations on the zinc sulphide screen. Observations of this experiment are as follows.
(I) Most of the a-particles passed through the foil without deflection.
(II) Only about 0.14% of the incident a-particles scattered by more than 1°.
(III) Only about one a-particle in every 8000 a-particles deflected by more than 90°.
These observations led to many arguments and conclusions which laid down the structure of the nuclear model of an atom.

(i) Rutherford's atomic model can be visualised as

(ii) Gold foil used in Geiger-Marsden experiment is about 10^-8 m thick. This ensures

(iii) In Geiger-Marsden scattering experiment, the trajectory traced by an a-particle depends on

(iv) In the Geiger-Marsden scatteririg experiment, in case of head-on collision, the impact parameter should be

(v) The fact only a small fraction of the number of incident particles rebound back in Rutherford scattering indicates that

At room temperature, most of the H-atoms are in ground state. When an atom receives some energy (i.e., by electron collisions), the atom may acquire sufficient energy to raise electron to higher energy state. In this condition, the atom is said to be in excited state. From the excited state, the electron can fall back to a state of lower energy emitting a photon equal to the energy difference of the orbit.

In a mixture of H-He⁺ gas (He+ is single ionized He atom), H-atoms and He⁺ ions are excited to their respective first excited states. Subsequently, H-atoms transfer their total excitation energy to He⁺ ions (by collisions).
(i) The quantum number n of the state finally populated in He⁺ ions is

(ii) The wavelength of light emitted in the visible region by He⁺ ions after collisions with H-atoms is

(iii) The ratio of kinetic energy of the electrons for the H-atoms to that of He⁺ ion for n = 2 is

(iv) The radius ofthe ground state orbit of H-atoms is

(v) Angular momentum of an electron in H-atom in first excited state is

Bohr's model explains the spectral lines of hydrogen atomic emission spectrum. While the electron of the atom remains in the ground state, its energy is unchanged. When the atom absorbs one or more quanta of energy, the electrons moves from the ground state orbit to an excited state orbit that is further away.

The given figure shows an energy level diagram of the hydrogen atom. Several transitions are marked as I, II, III and so on. The diagram is only indicative and not to scale.
(i) In which transition is a Balmer series photon absorbed?

(ii) The wavelength of the radiation involved in transition II is

(iii) Which transition will occur when a hydrogen atom is irradiated with radiation of wavelength 103 nm?

(iv) The electron in a hydrogen atom makes a transition from n = n₁ to n = n₂ state. The time period of the electron in the initial state is eight times that in the final state. The possible values of n₁ and n₂ are

(v) The Balmer series for the H-atom can be observed

The spectral series of hydrogen atom were accounted for by Bohr using the relation \(\bar{v}=R\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)\), 
where R = Rydberg constant = 1.097 x 10⁷ m.
Lyman series is obtained when an electron jumps to first orbit from any subsequent orbit. Similarly, Balmer series is obtained when an electron jumps to 2^nd orbit from any subsequent orbit, Paschen series is obtained when an electron jumps to 3^rd orbit from any subsequent orbit. Whereas Lyman series lies in U.V. region, Balmer series is in visible region and Paschen series lies in infrared region. Series limit is obtained when n₂ = \(\infty\)
(i) The wavelength of first spectral line of Lyman series is

(ii) The wavelength limit of Lyman series is

(iii) The frequency of first spectral line of Balmer series is

(iv) Which of the following transitions in hydrogen atoms emit photons of highest frequency?

(v) The ratio of minimum to maximum wavelength in Balmer series is

Photoelectric effect is the phenomenon of emission of electrons from a metal surface, when radiations of suitable frequency fallon them. The emitted electrons are called photoelectrons and the current so produced is called photoelectric current.
(i) With the increase of intensity of incident radiations on photoelectrons emitted by a photo tube, the number of photoelectrons emitted per unit time is

(ii) It is observed that photoelectron emission stops at a certain time t after the light source is switched on. The stopping potential (V) can be represented as

(iii) A point source of light of power 3.2 x 10^-3 W emits monoenergetic photons of energy 5.0 eV and work function 3.0 eV. The efficiency of photoelectron emission is 1 for every 10⁶ incident photons. Assume that photoelectrons are instantaneously swept away after emission. The maximum kinetic energy of photon is

(iv) Which of the following device is the application of Photoelectric effect?

(v) If the frequency of incident light falling on a photosensitive metal is doubled, the kinetic energy of the emitted photoelectron is

When a monochromatic radiations of suitable frequency obtained from source S, after being filtered by a filter attached on the window W, fall on the photosensitive place C, the photo electrons are emitted from C, which get accelerated towards the plate A if it is kept at positive potential. These electrons flow in the outer circuit resulting in photoelectric current. Due to it, the micro ammeter shows a deflection. The reading of micrommeter measures the photoelectric current.

An experimental setup of verification of photoelectric effect is shown in figure. The voltage across the electrodes is measured with the help of an ideal voltmeter, and which can be varied by moving jockey J on the potentiometer wire. The battery used in potentiometer circuit is of 16 V and its internal resistance is 2 \(\Omega\)  The resistance of 100 ern long po.t•e. ntiometer wire is 8 \(\Omega\).

The photocurrent is measured with the help of an ideal ammeter. Two plates of potassium oxide of area 50 cm² at separation 0.5 mm are used in the vacuum tube. Photocurrent in the circuit is very small, so we can treat the
potentiometer circuit as an independent circuit

(i) When radiation falls on the cathode plate, a current of 2 \(\mu \)A is recorded in the ammeter. Assuming that the vacuum tube setup follows Ohm's law, the equivalent resistance of vacuum tube operating in the case when jockey is at end P is

(ii) It is found that ammeter current remains unchanged (2 \(\mu\)A) even when the jockey is moved from the end P to the middle point of the potentiometer wire. Assuming that all the incident photons eject electrons and the power of the light incident is 4 x 10^-6\(\Omega\)Then, the color of the incident light is

(iii) Which of the following colors may not give photoelectric effect for this cathode?

(iv) When other light falls on the anode plate, the ammeter reading zero till jockey is moved from the end P to the middle point of the wire PQ. Therefore, the deflection is recorded in the ammeter. The maximum kinetic energy of the emitted electron is

(v) If the intensity of incident radiation is increased twice, the number of photoelectrons emitted per second will be

A point source S of power 6.4 x 10^-3W emits mono energetic photons each of energy 6.0 eV. The source is located at a distance of 0·8 m from the centre of a stationary metallic sphere of work function 3·0 eV and of radius 1.6 x 10^-3 m as shown in figure. The sphere is isolated and initially neutral and photoelectrons are instantly taken away from sphere after emission. The efficiency of photoelectric emission is one for very 10⁵ incident photons.

(i) The'power received by the sphere through radiations is

(ii) Number of photons striking the metal sphere per second is

(iii) The number of photoelectrons emitted per second is about

(iv) The photoelectric emission stops when the sphere acquires a potential about

(v) If the distance of source becomes double from the centre of the metal sphere then the power received by the sphere

According to Einstein, when a photon of light of frequency u or wavelength \(\lambda\) is incident on a photosensitive metal surface of work function \(\phi\)₀w' here \(\phi\)₀< hv (here, h is Planck's constant), then the emission of photoelectrons takes place. The maximum kinetic energy of the emitted photoelectrons is given by K_max = hv - \(\phi\)₀. If the frequency of the incident light is V₀ called threshold frequency, the photoelectrons are emitted from metal without any kinetic energy. So hv₀ = \(\phi\)
(i) A metal of work function 3·3 eV is illuminated by light of wavelength 300 nm. The maximum kinetic energy of photoelectrons emitted is (taking h = 6·6 x 10^-34 Js)

(ii) The variation of maximum kinetic energy (K_max) of the emitted photoelectrons with frequency (v) of the incident radiations can be represented by

(iii) The variation of photoelectric current (i) with the intensity of the incident radiation (I) can be represented by

(iv) The graph between the stopping potential (V₀) and \(\left(\frac{1}{\lambda}\right)\) is shown in the figure \(\phi_{1}, \phi_{2}, \phi_{3}\) 3 are work function. Which of the following options is correct?

(v) Which of the following figures represent the variation of particle momentum and the associated de- Broglie wavelength?

When light of sufficiently high frequency is incident on a metallic surface, electrons are emitted from the metallic surface. This phenomenon is called photoelectric emission. Kinetic energy of the emitted photoelectrons depends on the wavelength of incident light and is independent of the intensity of light. Number of emitted photoelectrons depends on intensity. (hv - \(\phi\) is the maximum kinetic energy of emitted photoelectrons (where \(\phi\) is the work function of metallic surface). Reverse effect of photo emission produces X-ray. X-ray is not deflected by electric and magnetic fields. Wavelength of a continuous X-ray depends on potential difference across the tube. Wavelength of characteristic X-ray depends on the atomic number.
(i) Einstein's photoelectric equation is

(ii) Light of wavelength \(\lambda\) which is less than threshold wavelength is incident on a photosensitive material. If incident wavelength is decreased so that emitted photoelectrons are moving with some velocity then stopping potential will

(iii) When ultraviolet rays incident on metal plate then photoelectric effect does not occur, it occur by incident of

(iv) If frequency (v > v₀) of incident light becomes n times the initial frequency (v), then K.E. of the emitted photoelectrons becomes (v₀ threshold frequency).

(v) A monochromatic light is used in a photoelectric experiment. The stopping potential

If double slit apparatus is immersed in a liquid of refractive index, I-l the wavelength of light reduces to \(\lambda\) and fringe width also reduces to \(\beta^{\prime}=\frac{\beta}{\mu} \text { . }\)
The given figure shows a double-slit experiment in which coherent monochromatic light of wavelength A from a distant source is incident upon the two slits, each of width w(w >> \(\lambda\)) and the interference pattern is viewed on a distant screen. A thin piece of glass of thickness t and refractive index n is placed between one of the slit and the screen, perpendicular to the light path.

(i) In Young's double slit interference pattern, the fringe width

(ii) If the width w of one of the slits is increased to 2w, the become the amplitude due to slit

(iii) In YDSE, let A and B be two slits. Films of thicknesses t_A and t_B and refractive indices m_A and m_B are placed in front of A and B, respectively. If \(\mu_{\mathrm{A}} t_{A}=\mu_{B} t_{B}\) then the central maxima will

(iv) In Young's double slit experiment, a third slit is made in between the double slits. Then

(v) In Young's double slit experiment, if one of the slits is covered with a microscope cover slip, then

Distance between two successive bright or dark fringes is called fringe width.
\(\beta=Y_{n+1}-Y_{n}=\frac{(n+1) \lambda D}{d}-\frac{n \lambda D}{d}=\frac{\lambda D}{d}\)
Fringe width is independent of the order of the maxima. If whole apparatus is immersed in liquid of refractive index \(\mu\) then \(\beta=\frac{\lambda D}{\mu d}\) (fringe width decreases). Angular fringe width (\(\theta\)) is the angular separation between two consecutive maxima or minima \(\theta=\frac{\beta}{D}=\frac{\lambda}{d}\)
In the arrangement shown in figure, slit S₃ and S₄ are having a variable separation Z. Point 0 on the screen is at the common perpendicular bisector of S₁S₂ and S₃S₄.

(i) The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double-slit experiment, is

(ii) In Young's double - slit experiment if yellow light is replaced by blue light, the interference fringes become

(iii) In Young's double slit experiment, if the separation between the slits is halved and the distance between the slits and the screen is doubled, then the fringe width compared to the unchanged one will be

(iv) When the complete Young's double slit experiment is immersed in water, the fringes

(v) In a two slit experiment with white light, a white fringe is observed on a screen kept behind the slits. When the screen is moved away by 0.05 m, this white fringe

When light from a monochromatic source is incident on a single narrow slit, it gets diffracted and a pattern of alternate bright and dark fringes is obtained on screen, called "Diffraction Pattern" of single slit. In diffraction pattern of single slit, it is found that
(I) Central bright fringe is ·of maximum intensity and the intensity of any secondary bright fringe decreases with increase in its order.
(II) Central bright fringe is twice as wide as any other secondary bright or dark fringe .

(i) A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 A and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is

(ii) In Fraunhofer diffraction pattern, slit width is 0.2 mm and screen is at 2 m away from the lens. If wavelength of light used is 5000 \(\lambda\) then the distance between the first minimum on either side the central maximum is

(iii) Light of wavelength 600 nm is incident normally on a slit of width 0.2 mm. The angular width of central maxima in the diffraction pattern is (measured from minimum to minimum)

(iv) A diffraction pattern is obtained by using a beam of red light. What will happen, if the red light is replaced by the blue light?

(v) To observe diffraction, the size of the obstacle

In Young's double slit experiment, the width of the central bright fringe is equal to the distance between the first dark fringes on the two sides of the central bright fringe.
In given figure below a screen is placed normal to the line joining the two point coherent source SI and S_2' The interference pattern consists of concentric circles.

(i) The optical path difference at P is

(ii) Find the radius of the n^th bright fringe.

(iii) If d = 0.5 mm, \(\lambda\)= 5000 \(\dot A \)and D = 100 em, find the value of n for the closest second bright fringe

(iv) The coherence of two light sources means that the light waves emitted have

(v) The phenomenon of interference is shown by

A narrow tube is bent in the form of a circle of radius R, as shown in figure. Two small holes S and D are made in the tube at the positions at right angle to each other. A source placed at S generates a wave of intensity Io which is equally divided into two parts: one part travels along the longer path, while the other travels along the shorter path. Both the waves meet at point D where a detector is placed.

(i) If a maxima is formed at a detector, then the magnitude of wavelength \(\lambda\) of the wave produced is given by

(ii) If the intensity ratio of two coherent sources used in Young's double slit experiment is 49 : 1, then the ratio between the maximum and minimum intensities in the interference pattern is

(iii) The maximum intensity produced at D is given by

(iv) In a Young's double slit experiment, the intensity at a point where the path difference is \(\lambda\)/6 (\(\lambda\) - wavelength of the light) is I. If I₀ denotes the maximum intensity, then I/I₀ is equal to

(v) Two identical light waves, propagating in the same direction, have a phase difference d. After they superpose the intensity of the resulting wave will be proportional to

A convex or converging lens is thicker at the centre than at the edges. It converges a parallel beam of light on refraction through it. It has a real focus. Convex lens is of three types:
(i) Double convex lens
(ii) Plano-convex lens
(iii) Concavo-convex lens. Concave lens is thinner at the centre than at the edges. It diverges a parallel beam of light on refraction through it. It has a virtual focus.
(i) A point object 0 is placed at a distance of 0.3 m from a convex lens (focal length 0.2 m) cut into two halves each of which is displaced by 0.0005 m as shown in figure.What will be the location of the image?

(ii) Two thin lenses are in contact and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, the focal length of the other would be

(iii) A spherical air bubble is embedded in a piece of glass. For a ray of light passing through the bubble, it behaves like a

(iv) Lens used in magnifying glass is

(v) The magnification of an image by a convex lens is positive only when the object is placed

Power (P) of a lens is given by-reciprocal of focal length (f) of the lens i.e., \(P=\frac{1}{f}\) where fis in metre and P is in dioptre. For a convex lens, power is positive and for a concave lens, power is negative. When a number of thin lenses of powers P₁, P₂, P₃, .....are held in contact with one another, the power of the combination is given by algebraic sum of the powers of all the lenses i.e., P = P₁ + P₂ + P₃ + ....
(i) A convex and a concave lens separated by distance d are then put in contact. The focal length of the combination

(ii) If two lenses of power +1.5D and +1.0D are placed in contact, then the effective power of combination will be

(iii) If the power of a lens is +5 dioptre, what is the focal length of the lens?

(iv) Two thin lenses offocallengths +10 cm and -5 em are kept in contact. The power of the combination is

(v) A convex lens of focal length 25 cm is placed coaxially in contact with a concave lens of focal length 20 cm. The system will be

Total internal reflection is the phenomenon of reflection of light into denser medium at the interface of denser medium with a rarer medium. For this phenomenon to occur necessary condition is that light must travel from denser to rarer and angle of incidence in denser medium must be greater than critical angle (C) for the pair of media in contact. Critical angle depends on nature of medium and wavelength of light. We can show that
\(\mu=\frac{1}{\sin C} .\)
(i) Critical angle for glass air interface, where \(\mu\) of glass is \(\frac{3}{2}\) is

(ii) Critical angle for water air interface is 48.6°. What is the refractive index of water?

(iii) Critical angle for air water interface for violet colour is 49°. Its value for red colour would be

(iv) Which of the following is not due to total internal reflection?

(v) Critical angle of glass is \(\theta\)₁ and that of water is \(\theta\)₂, The critical angle for water and glass surface would be \(\left(\mu_{g}=3 / 2, \mu_{w}=4 / 3\right)\)

The lens maker's formula is a relation that connects focal length of a lens to radii of curvature of two surfaces of the lens and refractive index of the material of the lens. It is \(\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\) where \(\mu\) is refractive index oflens material w.r.t. the medium in which lens is held.As ,\(\mu_{v}>\mu_{r}\) therefore \(f_{r}>f_{v^{\prime}}\) Mean focal length of lens for yellow colour is \(f=\sqrt{f_{r} \times f_{v}}\).
(i) Focal length of a equiconvex lens of glass \(\mu=\frac{3}{2}\) in air is 20 cm. The radius of curvature of each surface is

(ii) A substance is behaving as convex lens in air and concave in water, then its refractive index is

(iii) For a thin lens with radii of curvatures R₁ and R₂, refractive index nand focal length f, the factor \(\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\) is equal to

(iv) A given convex lens of glass \(\left(\mu=\frac{3}{2}\right)\) can behave as concave when it is held in a medium of \(\mu\) equal to

(v) The radii of curvature of the surfaces of a double convex lens are 20 cm and 40 cm respectively, and its focal length is 20 cm. What is the refractive index of the material of the lens?

An astronomical telescope is an optical instrument which is used for observing distinct images of heavenly bodies libe stars, planets etc. It consists of two lenses. In normal adjustment of telescope, the final image is formed at infinity. Magnifying power of an astronomical telescope in normal adjustment is defined as the ratio of the angle subtended at the eye by the angle subtended at the eye by the final image to the angle subtended at the eye, by the object directly, when the final image and the object both lie at infinite distance from the eye. It is given by,\(m=\frac{f_{0}}{f_{e}}\) To increase magnifying power of an astronomical telescope in normal adjustment, focal length of objective lens should be large and focal length of eye lens should be small.
(i) An astronomical telescope of magnifying power 7 consists of the two thin lenses 40 cm apart, in normal adjustment. The focal lengths of the lenses are

(ii) An astronomical telescope has a magnifying power of 10. In normal adjustment, distance between the objective and eye piece is 22 cm. The focal length of objective lens is

(iii) In astronomical telescope compare to eye piece, objective lens has

(iv) To see stars, use

(v) For large magnifying power of astronomical telescope

In an electromagnetic wave both the electric and magnetic fields are perpendicular to the direction of propagation, that is why electromagnetic waves are transverse in nature. Electromagnetic waves carry energy as they travel through space and this energy is shared equally by the electric and magnetic fields. Energy density of an electromagnetic waves is the energy in unit volume of the space through which the wave travels.
(i) The electromagnetic waves propagated perpendicular to both \(\vec{E} \text { and } \vec{B}\). The electromagnetic waves travel in the direction of

(ii) Fundame tal particle in an electromagnetic wave is

(iii) Electromagnetic waves are transverse in nature is evident by

(iv) For a wave propagating in a medium, identify the property that is independent of the others.

(v) The electric and magnetic fields of an electromagnetic waves are

Maxwell showed that the speed of an electromagnetic wave depends on the permeability and permittivity of the medium through which it travels. The speed of an electromagnetic wave in free space is given by \(c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} .\)The fact led Maxwell to predict that light is an electromagnetic wave. The emergence of the speed of light from purely electromagnetic considerations is the crowning achievement of Maxwell's electromagnetic theory. The speed of an electromagnetic wave in any medium of permeability \(\mu\) and permittivity \(\varepsilon\) will be \(\frac{c}{\sqrt{K \mu_{r}}}\) where K is the dielectric constant of the medium and \(\mu_r\) is the relative permeability.
(i) The dimensions of \(\frac{1}{2} \varepsilon_{0} E^{2}\) (\(\varepsilon_o\) permittivity of free space; E = electric field) is

(ii) Let [\(\varepsilon\)₀] denote the dimensional formula of the permittivity of the vacuum. If M = mass, L = length, T = time and A = electric current, then

(iii) An electromagnetic wave of frequency 3MHz passes from vacuum into a dielectric medium with permittivity \(\varepsilon\) = 4. Then

(iv) Which of the following are not electromagnetic waves?

(v) The electromagnetic waves travel with

An electromagnetic wave transports linear momentum as it travels through space. If an electromagnetic wave transfers a total energy U to a surface in time t, then total linear momentum delivered to the surface is \(p=\frac{U}{c}\) When an electromagnetic wave falls on a surface, it exerts pressure on the surface. In 1903, the American scientists Nichols and Hull succeeded in measuring radiation pressures of visible light where other had failed, by making a detailed empirical analysis of the ubiquitous gas heating and ballistic effects.
(i) The pressure exerted by an electromagnetic wave of intensity I (W m^-2) on a non-reflecting surface is (c is the velocity of light)

(ii) Light with an energy flux of 18 W/cm² falls on a non-reflecting surface at normal incidence. The pressure exerted on the surface is

(iii) Radiation of intensity 0.5 W m^-2 are striking a metal plate. The pressure on the plate is

(iv) A point source of electromagnetic radiation has an average power output of 1500 W The maximum value of electric field at a distance of3 m from this source (in V m^-1) is

(v) The radiation pressure of the visible light is of the order of

All the known radiations from a big family of electromagnetic waves which stretch over a large range of wavelengths. Electromagnetic wave include radio waves, microwaves, visible light waves, infrared rays, UV rays, X-rays and gamma rays. The orderly distribution of the electromagnetic waves in accordance with their wavelength or frequency into distinct groups having widely differing properties is electromagnetic spectrum.
(i) Which wavelength of the Sun is used finally as electric energy?

(ii) Which of the following electromagnetic radiations have the longest wavelength?

(iii) Which one of the following is not electromagnetic in nature?

(iv) Which of the following has minimum wavelength?

(v) The decreasing order of wavelength of infrared, microwave, ultraviolet and gamma rays is

Electrons oscillating in a circuit give rise to radiowaves. A transmitting antenna radiates most effectively the radiowaves of wavelength equal to the size of the antenna. The infrared waves incident on a substance set into oscillation all its electrons, atoms and molecules. This increases the internal energy and hence the temperature of the substance.
(i) If v_g, v_x and vm are the speeds of gamma rays, X-rays and microwaves respectively in vacuum, then

(ii) Which of the following will deflect in electric field?

(iii) \(\Upsilon\)-rays are detected by

(iv) The frequency of electromagnetic wave, which best suited to observe a particle of radius 3 x 10^-4 cm is the order of

(v) We consider the radiation emitted by the human body. Which one of the following statements is true?

When a pure resistance R, pure inductor L and an ideal capacitor of capacitance C is connected in series to a source of alternating e.m.f., then current at any instant through the three elements has the same amplitude and is represented as I = I_osinwt. However, voltage across each element has a different phase relationship with the current as shown in graph.
The effective resistance of RLC circuit is called impedance (2) of the circuit and the voltage leads the current by a phase angle \(\phi .\)

A resistor of \(12 \Omega\) a capacitor of reactance \(14 \Omega\) and a pure inductor of inductance 0.1 H are joined in series and placed across 200 V, 50 Hz a.c. supply
(i) The value of inductive reactance is

(ii) The value of impedance is

(iii) What is the value of current in the circuit?

(iv) What is the value of the phase angle between current and voltage?

(v) From graph, which one is true from following?

Let a source of alternating e.m.f. E = E_osinrot be connected to a capacitor of capacitance C. If 'I' is the instantaneous value of current in the circuit at instant t, then \(I=\frac{E_{0}}{1 / \omega C} \sin \left(\omega t+\frac{\pi}{2}\right)\) The capacitive reactance limits the amplitude of current in a purely capacitive circuit and it is given by \(X_{C}=\frac{1}{\omega C}\) 

(i) What is the unit of capacitive reactance?

(ii) The capacitive reactance of a \(5 \mu \mathrm{F}\) lFcapacitor for a frequency of 10⁶ Hz is

(iii) In a capacitive circuit, resistance to the flow of current is offered by

(iv) In a capacitive circuit, by what value of phase angle does alternating current leads the e.m.f?

(v) One microfarad capacitor is joined to a 200 V, 50 Hz alternator. The rms current through capacitor is

Let a source of alternating e.m.f E = E_osinrot be connected to a circuit containing a pure inductance L. If I is the value of instantaneous current in the circuit, then \(I=I_{0} \sin \left(\omega t-\frac{\pi}{2}\right)\).The inductive reactance limits the current in a purely inductive circuit and is given by \(X_{L}=\omega L\)

(i) A 100 hertz a.c. is flowing in a 14 mH coil. The reactance is 

(ii) In a pure inductive circuit, resistance to the flow of current is offered by

(iii) In a inductive circuit, by what value of phase angle does alternating current lags behind e.m.f.?

(iv) How much inductance should be connected to 200 V, 50 Hz a.c. supply so that a maximum current of 0.9 A  flows through it?

(v) The maximum value of current when inductance of 2 H is connected to 150 volt, 50 Hz supply is

The power averaged over one full cycle of a.c. is known as average power. It is also known as true power 
\(P_{\mathrm{av}}=V_{\mathrm{rms}} I_{\mathrm{rms}} \cos \phi=\frac{V_{0} I_{0}}{2} \cos \phi\)
Root mean square or simply rms watts refer to continuous power
A circuit containing a 80.mH inductor and a \(60 \mu \mathrm{F}\) capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.

(i) The value of current amplitude is

(ii) Find rms value.

(iii) The average power transferred to inductor is

(iv) The average power transferred to the capacitor is

(v) What is the total average power absorbed by the circuit?

A transformer is essentially an a.c. device. It cannot work on d.c. It changes alternating voltages or currents. It does not affect the frequency of a.c. It is based on the phenomenon of mutual induction. A transformer essentially consists of two coils of insulated copper wire having different number of turns and wound on the same soft iron core. 
The number of turns in the primary and secondary coils of an ideal transformer are 2000 and 50 respectively. The primary coil is connected to a main supply of 120 V and secondary coil is connected to a bulb of resistance \(0.6 \Omega\)
(i) The value of voltage across the secondary coil is

(ii) The value of current in the bulb is

(iii) The value of current in primary coil is

(iv) Power in primary coil is

(v) Power in secondary coil is

Lenz's law states that the direction of induced current in a circuit is such that it opposes the change which produces it. Thus, if the magnetic flux linked with a closed circuit increases, the induced current flows in such a direction that magnetic flux is created in the opposite direction of the original magnetic flux. If the magnetic flux linked with the closed circuit decreases, the induced current flows in such a direction so as to create magnetic flux in the direction of the original flux.

(i) Which of the following statements is correct?

(ii) The polarity of induced emf is given by

(iii) Lenz's law is a consequence of the law of conservation of

(iv) Near a circular loop of conducting wire as shown in the figure, an electron moves along a straight line. The direction of the induced current if any in the loop is

(v) Two identical circular coils A and B are kept in a horizontal tube side by side without touching each other. If the current in coil A increases with time, in response, the coil B.

Mutual inductance is the phenomenon of inducing emf in a coil, due to a change of current in the neighbouring coil. The amount of mutual inductance that links one coil to another depends very much on the relative positioning of the two coils, their geometry and relative separation between them. Mutual inductance between the two coils increases \(\mu_{r}\) times if the coils are wound over an iron core of relative permeability \(\mu_{r}\).

(I) A short solenoid of radius a, number of turns per unit length nI' and length L is kept coaxially inside a very long solenoid of radius b, numbdr of turns per unit length n₂• What is the mutual inductance of the system?

(ii) If a change in current of 0.01 A in one coil produces a change in magnetic flux of 2 x l0^-2 weber in another coil, then the mutual inductance between coils is

(iii) Mutual inductance of two coils can be increased by

(iv) When a sheet of iron is placed in between the two co-axial coils, then the mutual inductance between the coils will

(v) The SI unit of mutual inductance is

Currents can be induced not only in conducting coils, but also in conducting sheets or blocks. Current is induced in solid metallic masses when the magnetic flux threading through them changes. Such currents flow in the form of irregularly shaped loops throughout the body of the metal. These currents look like eddies or whirlpools in water so they are known as eddy currents. Eddy currents have both undesirable effects and practically useful applications. For example it causes unnecessary heating and wastage of power in electric motors, dynamos and in the cores of transformers.
(I) The working of speedometers of trains is based on

(ii) Identify the wrong statement

(iii) Which of the following is the best method to reduce eddy currents?

(iv) The direction of eddy currents is given by

(v) Eddy currents can be used to heat localised tissues of the human body. This branch of medical therapy is called 

When a current I flows through a coil, flux linked with it is \(\phi=L I,\) where L is a constant known as self-inductance of the coil. Any change in current sets up an induced emf in the coil. Thus, self-inductance of a coil is the induced emf set up in it when the current passing through it changes at the unit rate. It is a measure of the opposition to the growth or the decay of current flowing through the coil. Also, value of self-inductance depends on the number of turns in the solenoid, its area of cross-section, and the relative permeability of its core material.

(I) The inductance in a coil plays the same role as 

(ii) A current of 2.5 A flows through a coil of inductance 5 H. The magnetic flux linked with the coil is

(iii) The inductance L of a solenoid depends upon its radius R as

(iv) The unit of self-inductance is

(v) The induced e.m.f in a coil of 10 henry inductance in which current varies from 9 A to 4 A in 0.2 second is

In year 1820 Oersted discovered the magnetic effect of current. Faraday gave the thought that reverse of this phenomenon is also possible i.e., current can also be produced by magnetic field. Faraday showed that when we move a magnet towards the coil which is connected by a sensitive galvanometer. The galvanometer gives instantaneous deflection showing that there is an electric current in the loop.
Whenever relative motion between coil and magnet takes place an emf induced in coil. If coil is in closed circuit then current is also induced in the circuit. This phenomenon is called electromagnetic induction.

(I) The north pole of a long bar magnet was pushed slowly into a short solenoid connected to a galvanometer. The magnet was held stationary for a few seconds with the north pole in the middle of the solenoid and then withdrawn rapidly. The maximum deflection of the galvanometer was observed when the magnet was

(ii) Two similar circular loops carry equal currents in the same direction. On moving the coils further apart, the electric current will

(iii) A closed iron ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is

(iv) Whenever there is a relative motion between a coil and a magnet, the magnitude of induced emf set up in the coil does not depend upon the

(v) A coil of metal wire is kept stationary in a non-uniform magnetic field

The earth's magnetic field at a point on its surface is usually characterised by three quantities: (a) declination (b) inclination or dip and (c) horizontal component of the field. These are known as the elements of the earth's magnetic field. At a place, angle between geographic meridian and magnetic meridian is defined as magnetic declination, whereas angle made by the earth's magnetic field with the horizontal in magnetic meridian is known as magnetic dip.

(i) In a certain place, the horizontal component of magnetic field is \(\frac{1}{\sqrt{3}}\) times the vertical component. The angle of dip at this place is 

(ii) The angle between the true geographic north and the north shown by a compass needle is called as

(iii) The angles of dip at the poles and the equator respectively are

(iv) A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It

(v) Select the correct statement from the following

By analogy to Gauss's law of electrostatics, we can write Gauss's law of magnetism as \(\oint \vec{B} \cdot d \vec{s}=\mu_{0} m_{\text {inside }}\) where \(\oint \vec{B} \cdot d \vec{s}\) is the magnetic flux and \(m_{\text {inside }}\) is the net pole strength inside the closed surface.
We do not have an isolated magnetic pole in nature. At least none has been found to exist till date. The smallest unit of the source of magnetic field is a magnetic dipole where the net magnetic pole is zero. Hence, the net magnetic pole enclosed by any closed surface is always zero. Correspondingly, the flux of the magnetic field through any closed surface is zero.

(I) Consider the two idealised systems
(i) a parallel plate capacitor with large plates and small separation and
(ii) a long solenoid oflength L >> R, radius of cross-section.
In (i) \(\vec{E}\) is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zerq outside. These idealised assumptions, however, contradict fundamental laws as below

(ii) The net magnetic flux through any closed surface, kept in a magnetic field is

(iii) A closed surface S encloses a magnetic dipole of magnetic moment 2ml. The magnetic flux emerging from the surface is

(iv) Which of the following is not a consequence of Gauss's law?

(v) The surface integral of a magnetic field over a surface

When the atomic dipoles are aligned partially or fully, there is a net magnetic moment in the direction of the field in any small volume of the material. The actual magnetic field inside material placed in magnetic field is the sum of the applied magnetic field and the magnetic field due to magnetisation. This field is called magnetic intensity (H).
\(H=\frac{B}{\mu_{0}}-M\)
where M is the magnetisation of the material, llo is the permittivity of vacuum and B is the total magnetic field. The measure that tells us how a magnetic material responds to an external field is given by a dimensionless quantity is appropriately called the magnetic susceptibility: for a certain class of magnetic materials, intensity of magnetisation is directly proportional to the magnetic intensity.
(i) Magnetization of a sample is

(ii) Identify the wrongly matched quantity and unit pair.

(iii) A bar magnet has length- 3 cm, cross-sectional area 2 cm² and magnetic moment 3 A m². The intensity of magnetisation of bar magnet is

(iv) A solenoid has core of a material with relative permeability 500 and its windings carry a current of 1 A. The number of turns of the solenoid is 500 per metre. The magnetization of the material is nearly

(v) The relative permeability of iron is 6000. Its magnetic susceptibility is

The magnetic field lines of the earth resemble that of a hypothetical magnetic dipole located at the centre of the earth. The axis of the dipole is presently tilted by approximately 11.3^o with respect to the axis of rotation of the earth.

The pole near the geographic North pole of the earth is called the North magnetic pole and the pole near the geographic South pole is called South magnetic pole.
(i) The strength of the earth's magnetic field varies from place to place on the earth's surface, its value being of the order of

(ii) A bar magnet is placed North-South with its North-pole due North. The points of zero magnetic field will be in which direction from centre of magnet?

(iii) The value of angle of dip is zero at the magnetic equator because on it

(iv) The angle of dip at a certain place, where the horizontal and vertical components of the earth's magnetic field are equal, is

(v) At a place, angle of dip is 30°. If horizontal component of earth's magnetic field is H, then the total intensity of magnetic field will be

The field of a hollow wire with constant current is homageneous
Curves in the graph shown give, as functions of radius distance r, the magnitude B of the magnetic field inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels.

(i) Which wire has the greatest magnitude of the magnetic field on the surface?

(ii) The current density in a wire a is

(iii) Which wire has the greatest radius?

(iv) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

(v) In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite direction. The magnetic field is zero

Various methods can be used to measure the mass of an atom. One possibility is through the use of a mass spectrometer. The basic feature of a Banbridge mass spectrometer is illustrated in figure. A particle carrying a charge +q is first sent through a velocity selector and comes out with velocity v = E/B.
The applied electric and magnetic fields satisfy the relation E = vB so that the trajectory of the particle is a straight line. Upon entering a region where a second magnetic field \(\vec{B}_{0}\) pointing into the page has been applied, the particle will move in a circular path with radius r and eventually strike the photographic plate.

(i) In mass spectrometer, the ions are sorted out in which of the following ways?

(ii) Radius of particle in second magnetic field B_o is

(iii) Which of the following will trace a circular trajectory wit largest radius?

(iv) Mass of the particle in terms q, B_o, B,r and E is

(v) The particle comes out of velocity selector along a straight line, because

Ampere's law gives a method to calculate the magnetic field due to given current distribution. According to it, the circulation \(\oint \vec{B} \cdot d \vec{l}\) of the resultant magnetic field along a closed plane curve is equal to \(\mu_{0}\) times the total current crossing the area bounded by the closed curve provided the electric field inside the loop remains constant. Ampere's law is more useful under certain symmetrical conditions. Consider one such case of a long Straight wire with circular cross-section (radius R) carrying current I uniformly distributed across this cross-section.

(i) The magnetic field at a radial distance r from the centre of the wire in the region r > R, is

(ii) The magnetic field at a distance r in the region r < R is

(iii) A long straight wire of a circular cross section (radius a) carries a steady current I and the current I is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field B with distance r from the centre of the wire?

(iv) A long straight wire of radius R carries a steady current I. The current is uniformly distributed across its cross-section. The ratio of magnetic field at R/2 and 2R is

(v) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

The path of a charged particle in magnetic field depends upon angle between velocity and magnetic field.If velocity \(\vec{v}\) is at angle \(\theta\) to \(\vec{B}\) component of velocity parallel to magnetic field \((v \cos \theta)\) remains constant and component of velocity perpendicular to magnetic field \((v \sin \theta)\) is responsible for circular motion, thus the charge particle moves in a helical path.

The plane of the circle is perpendicular to the magnetic field and the axis of the helix is parallel to the magnetic field. The charged particle. moves along helical path touching the line parallel to the magnetic field passing through the starting point after each rotation.
Radius of circular path is \(r=\frac{m v \sin \theta}{1 v_{q} B}\)
Hence the resultant path of the charged particle will be a helix, with its axis along the direction of \(\vec{B}\) as shown in figure.
(i) When a positively charged particle enters into a uniform magnetic field with uniform velocity, its trajectory can be (i) a straight line (ii) a circle (iii) a helix.

(ii) Two charged particles A and B having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of A makes an angle of 30° and that of B makes an angle of 90° with the field. Then the trajectory of

(iii) An electron having momentum 2.4 x 10^-23kg m/ s enters a region of uniform magnetic field of 0.15 T. The field vector makes an angle of 30° with the initial velocity vector of the electron. The radius of the helical path of the electron in the field shall be

(iv) The magnetic field in a certain region of space is given by \(\vec{B}=8.35 \times 10^{-2} \hat{i}\) T. A proton is shot into the field with velocity \(\vec{v}=\left(2 \times 10^{5} \hat{i}+4 \times 10^{5} \hat{j}\right) \mathrm{m} / \mathrm{s}\) The proton follows a helical path in the field. The distance moved by proton in the x-direction during the period of one revolution in the yz-plane will be
(Mass of proton = 1.67 x 10^-27kg)

(v) The frequency of revolution of the particle is

An electron with speed V_o << c moves in a circle ofradius r_o in a uniform magnetic field. This electron is able to traverse a circular path as magnetic field is perpendicular to the velocity of the electron. A force acts on the particle perpendicular to both \(\vec{v}_{0}\) and \(\vec{B}\). This force continuously deflects the particle sideways without  changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is T_o .

(i) If the speed of the electron is now doubled to 2v_o.The radius of the circle will change to

(ii) If v_o = 2v_o then the time required for one revolution of the electron will change to

(iii) A charged particles is projected in a magnetic field \(\vec{B}=(2 \hat{i}+4 \hat{j}) \times 10^{2} \mathrm{~T}\) The acceleration of the particle is found to be \(\vec{a}=(x \hat{i}+2 \hat{j}) \mathrm{m} \mathrm{s}^{-2}\). Find the value of x.

(iv) If the given electron has a velocity not perpendicular to B, then trajectory of the electron is

(v) If this electron of charge (e) is moving parallel to uniform magnetic field with constant velocity v, the force acting on the electron is

When a rectangular loop PQRS of sides 'a' and 'b' carrying current I is placed in uniform magnetic field \(\vec{B}\) such that area vector \(\vec{A}\) makes an angle \(\theta\) with direction of magnetic field, then forces on the arms QR and SP of loop are equal, opposite and collinear, thereby perfectly cancel each other, whereas forces on the arms PQ and RS of loop are equal and opposite but not collinear, so they give rise to torque on the loop.

Force on side PQ or RS ofloop is F = IbB sin 90° = Ib B and perpendicular distance between two non-collinear forces is \(r_{\perp}\) = a sin \(\theta\)

So, torque on the loop, \(\tau=I A B \sin \theta\)
In vector form torque \(\vec{\tau}=\vec{M} \times \vec{B}\)
where \(\vec{M}=N I \vec{A}\) is called magnetic dipole moment of current loop and is directed in direction of area vector \(\vec{A}\) i.e., normal to the plane ofloop.
(i) A circular loop of area 1 cm², carrying a current of 10 A is placed in a magnetic field of 0.1T perpendicular to the plane of the loop. The torque on the loop due to the magnetic field is

(ii) Relation between magnetic moment and angular velocity is

(ill) A current loop in a magnetic field

(iv) The magnetic moment of a current I carrying circular coil of radius r and number of turns N varies as

(v) A rectangular coil carrying current is placed in a non-uniform magnetic field. On that coil the total

(i) (c): In mass spectrometer, the ions are sorted out by accelerating them through electric and magnetic field.

Electrostatic potential energy of a system of point charges is defined as the total amount of work done in bringing the different charges to their respective positions from infinitely charge mutual separations. The work is stored in the system of two point charges in the form of electrostatic potential energy U of the system. Electric potential difference between any points A and B in an electric field is the amount of work done in moving a unit positive test charge from A to B along any path agents the electrostatic force
\(V_{B}-V_{A}=\frac{W_{A B}}{q_{0}}=\int \mid \vec{E} \cdot d l\)

(i) A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will

(ii) Which of the following statement is not true?

(iii) Work done in moving a charge from one point to another inside a uniformly charged conducting sphere is

(iv) The work done in bringing a unit positive charge from infinite distance to a point at distance x from a positive charge Q is W. Then the potential \(\phi\) at that point is

(v) If \(1 \mu C\) charge is shifted from A to B and it is found that work done by an external force is \(40 \mu \mathrm{J}\). In doing so against electrostatics force, the potential difference V_A- V_B is 

Potential difference (\(\Delta\)V) between two points A and B separated by a distance x, in a uniform electric field E is given by \(\Delta V=-E x\),where x is measured parallel to the field lines. If a charge qo moves from P to Q, the changein potential energy \((\Delta U)\) is given as \(\Delta U=q_{0} \Delta V .\) A proton is released from rest in uniform electric field of magnitude \(4.0 \times 10^{8} \mathrm{Vm}^{-1}\) directed along the positive X-axis. The proton undergoes a displacement of 0.25 m in the direction of E.
Mass of a proton = 1.66 x 10^-27 kg and charge of proton = 1.6 x10^-19 C

(i) The change in electric potential of the proton between the points A and B is

(ii) The change in electric potential energy of the proton for displacement from A to B is

(iii) The mutual electrostatic potential energy between two protons which are at a distance of 9 x 10^-15 m, in \({ }_{92} \mathrm{U}^{235}\) nucleus is

(iv) If a system consists of two charges 4 mC and -3mC with no external field placed at (-5 em, 0, 0) and (5 em, 0, 0) respectively. The amount of work required to separate the two charges infinitely away from each other is

(v) As the proton moves from P to Q, then

The potential at any observation point P of a static electric field is defined as the work done by the external agent (or negative of work done by electrostatic field) in slowly bringing a unit positive point charge from infinity to the observation point. Figure shows the potential variation along the line of charges. Two point charges Q₁ and Q₂ lie along a line at a distance from each other.

(i) At which of the points 1, 2 and 3 is the electric field is zero?

(ii) The signs of charges Q₁ and Q₂ respectively are

(iii) Which of the two charges Q₁ and Q₂ is greater in magnitude?

(iv) Which of the following statement is not true?

(v) Positive and negative point charges of equal magnitude are kept at \(\left(0,0, \frac{a}{2}\right)\) and \(\left(0,0, \frac{-a}{2}\right)\) respectively.
The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is

For the various charge systems, we represent equipotential surfaces by curves and line of force by full line curves. Between any two adjacent equipotential surfaces, we assume a constant potential difference the equipotential surfaces of a single point charge are concentric spherical shells with their centres at the point charge. As the lines of force point radially outwards, so they are perpendicular to the equipotential surfaces at all points.

(i) Identify the wrong statement.

(ii) Nature of equipotential surface for a point charge is

(iii) A spherical equipotential surface is not possible

(iv) The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is

(v) The work done to move a unit charge along an equipotential surface from P to Q

This energy possessed by a system of charges by virtue of their positions. When two like charges lie infinite distance apart, their potential energy is zero because no work has to be done in moving one charge at infinite distance from the other.
In carrying a charge q from point A to point B, work done \(W=q\left(V_{A}-V_{B}\right)\). This work may appear as change in KE/PE of the charge. The potential energy of two charges q₁ and q₂ at a distance r in air is \(\frac{q_{1} q_{2}}{4 \pi \varepsilon_{0} r}\). It is measured in joule. It may be positive, negative or zero depending on the signs of q_l and q₂.
(i) Calculate work done in separating two electrons form a distance of 1m to 2m in air, where e is electric charge and k is electrostatic force constant.

(ii) Four equal charges q each are placed at four corners of a square of side a each. Work done in carrying a charge -q from its centre to infinity is

(iii) Two points A and B are located in diametrically opposite directions of a point charge of +2 \(\mu \mathrm{C}\) at distances 2 m and 1 m respectively from it. The potential difference between A and B is 

(iv) Two point charges A = +3 nC and B = +1 nC are placed 5 ern apart in air. The work done to move charge B towards A by 1 cm is

(v) A charge Q is placed at the origin. The electric potential due to this charge at a given point in space is V. The work done by an external force in bringing another charge q from infinity up to the point is

The flow of charge in a particular direction constitutes the electric current. Current is measured in Ampere. Quantitatively, electric current in a conductor across an area held perpendicular to the direction of flow of charge is defined as the amount of charge is flowing across that area per unit time.
Current density at a point in a conductor is the ratio of the current at that point in the conductor to the area of cross section of the conductor of that point.
The given figure shows a steady current flows in a metallic conductor of non uniform cross section. Current density depends inversely on area, so, here \(J_{1}>J_{2}, \text { as } A_{1}.

(i) What is the current flowing through a conductor, if one million electrons are crossing in one millisecond through a cross-section of it ?

(ii) SI unit of electric current is

(iii) A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor?

(iv) A constant current I is flowing along the length of a conductor of variable cross-section as shown in the figure. The quantity which does not depend upon the area of cross-section is

(v) When a current of 40 A flows through a conductor of area 10 m², then the current density is

According to Ohm's law, the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor i.e \(I \propto V \Rightarrow \frac{V}{I}=R\) where R is resistance of the conductor Electrical resistance of a conductor is the obstruction posed by the conductor to the flow of electric current through it. It depends upon length, area of cross-section, nature of material and temperature of the conductor We can write \(R \propto \frac{l}{A} \text { or } R=\rho \frac{l}{A}\) where \(\rho\) is electrical resistivity of the material of the conductor.
(i) Dimensions of electric resistance is

(ii) If \(1 \mu \mathrm{A}\) current flows through a conductor when potential difference of2 volt is applied across its ends, then the resistance of the conductor is

(iii) Specific resistance of a wire depends upon

(iv) The slope of the graph between potential difference and current through a conductor is

(v) The resistivity of the material of a wire 1.0 m long, 0.4 mm in diameter and having a resistance of 2.0 ohm is

The resistance of a conductor at temperature t^oC is given by R_t = R_o (1 + \(\alpha\)t)
where R_t is the resistance at t^oC, R_o is the resistance at 0^oC and \(\alpha\) is the characteristics constants of the material of the conductor.
Over a limited range of temperatures, that is not too large. The resistivity of a metallic conductor is approximately given by \(\rho_{t}=\rho_{0}(1+\alpha t)\).
where \(\alpha\) is the temperature coefficient of resistivity. Its unit is \(\mathrm{K}^{-1} \text {or }{ }^{\circ} \mathrm{C}^{-1}\)
For metals, \(\alpha\) is positive i.e., resistance increases with rise in temperature.
For insulators and semiconductors, \(\alpha\) is negative i.e., resistance decreases with rise in temperature.

(i) Fractional increase in resistivity per unit increase in temperature is defined as

(ii) The material whose resistivity is insensitive to temperature is

(iii) The temperature coefficient of the resistance of a wire is 0.00125 per ^oC. At 300 K its resistance is 1 ohm. The resistance of wire will be 2 ohms at

(iv) The temperature coefficient of resistance of an alloy used for making resistors is

(v) For a metallic wire, the ratio V/I (V = applied potential difference and I = current flowing) is 

Emf of a cell is the maximum potential difference between two electrodes of the cell when no current is drawn from the cell. Internal resistance is the resistance offered by the electrolyte of a cell when the electric current flows through it. The internal resistance of a cell depends upon the following factors;
(i) distance between the electrodes
(ii) nature and temperature of the electrolyte
(iii) nature of electrodes
(iv) area of electrodes.

For a freshly prepared cell, the value of internal resistance is generally low and goes on increasing as the cell is put to more and more use. The potential difference between the two electrodes of a cell in a closed circuit is called terminal potential difference and its value is always less than the emf of the cell in a closed circuit. It can be written as V = E - Jr.
(i) The terminal potential difference of two electrodes of a cell is equal to emf of the cell when

(ii) A cell of emf E and internal resistance r gives a current of 0.5 A with an external resistance of \(12 \Omega\) and a current of 0.25 A with an external resistance of \(25 \Omega\) .What is the value of internal resistance of the cell?

(iii) Choose the wrong statement.

(iv) An external resistance R is connected to a cell of internal resistance r, the maximum current flows in the external resistance, when

(v) IF external resistance connected to a cell has been increased to 5 times, the potential difference across the terminals of the cell increases from 10 V to 30 V. Then, the emf of the cell is

Metals have a large number of free electrons nearly 10²⁸ per cubic metre. In the absence of electric field, average  terminal speed of the electrons in random motion at room temperature is of the order of 10⁵ m s^-1 When a potential difference V is applied across the two ends of a given conductor, the free electrons in the conductor experiences a force and are accelerated towards the positive end of the conductor. On their way, they suffer frequent collisions with the ions/atoms of the conductor and lose their gained kinetic energy. After each collision, the free electrons are again accelerated due to electric field, towards the positive end of the conductor and lose their gained kinetic energy in the next collision with the ions/atoms of the conductor. The average speed of the free electrons with which they drift towards the positive end of the conductor under the effect of applied electric field is called drift speed of the electrons.
(i) Magnitude of drift velocity per unit electric field is

(ii) The drift speed of the electrons depends on

(iii) We are able to obtain fairly large currents in a conductor because

(iv) Drift speed of electrons in a conductor is very small i.e., i = 10^-4 m s^-1. The Electric bulb glows immediately. When the switch is closed because

(v) The number density offree electrons in a copper conductor is 8.5 x 10²⁸ m^-3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10^-6m² and it is carrying a current of 3.0 A.

Coulomb's law states that the electrostatic force of attraction or repulsion acting between two stationary point charges is given by
\(F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}\)

where F denotes the force between two charges q₁ and q₂ separated by a distance r in free space, E_o is a constant known as permittivity of free space. Free space is vacuum and may be taken to be air practically.
If free space is replaced by a medium, then E_o is replaced by (E_ok) or (E_oEr)where k is known as dielectric constant or relative permittivity.
(i) In coulomb's law, F = \(k \frac{q_{1} q_{2}}{r^{2}}\), then on which of the following factors does the proportionality constant k depends?

(ii) Dimensional formula for the permittivity constant E_o of free space is

(iii) The force of repulsion between two charges of 1 C each, kept 1 m apart in vaccum is

(iv) Two identical charges repel each other with a force equal to 10 mgwt when they are 0.6 m apart in air. (g = 10 ms^-2). The value of each charge is

(v) Coulomb's law for the force between electric charges most closely resembles with

Smallest charge that can exist in nature is the charge of an electron. During friction it is only the transfer of electrons which makes the body charged. Hence net charge on any body is an integral multiple of charge of an electron.

[1.6 x 10^-19 C] i.e.                                  
q = ± ne
where n = 1,2,3,4, ....
Hence no body can have a charge represented as \(1.1 e, 2.7 e, \frac{3}{5} e, \text { etc. }\)
Recently, it has been discovered that elementary particles such as protons or neutrons are composed of more elemental units called quarks.
(i) Which of the following properties is not satisfied by an electric charge?

(ii) Which one of the following charges is possible?

(iii) If a charge on a body is 1 nC, then how many electrons are present on the body?

(iv) If a body gives out 10⁹ electrons every second, how much time is required to get a total charge of 1 C from it?

(v) A polythene piece rubbed with wool is found to have a negative charge of3.2 x 1O^-7C.Calculate the number of electrons transferred.

Net electric flux through a cube is the sum of fluxes through its six faces. Consider a cube as shown in figure,having sides oflength L = 10.0 cm. The electric field is uniform, has a magnitude E = 4.00 x 10³ N C^-I and is parallel to the xy plane at an angle of 37° measured from the +x-axis towards the +y-axis.

(i) Electric flux passing through surface S₆ is

(ii) Electric flux passing through surface s₁ is

(iii) The surfaces that have zero flux are

(iv) The total net electric flux through all faces of the cube is

(v) The dimensional formula of surface integral \(\oint \vec{E} \cdot d \vec{S}\)of an electric field is

When a charged particle is placed in an electric field, it experiences an electrical force. If this is the only force on the particle, it must be the net force. The net force will cause the particle to accelerate according to Newton's second law. So
\(\vec{F}_{e}=q \vec{E}=m \vec{a}\)

If \(\vec{E}\) is uniform, then \(\vec{a}\) is constant and \(\vec{a}=q \vec{E} / m\). If the particle has a positive charge, its acceleration is in the direction of the field. If the particle has a negative charge, its acceleration is in the direction opposite to the electric field. Since the acceleration is constant, the kinematic equations can be used.
(i) An electron of mass m, charge e falls through a distance h metre in a uniform electric field E. Then time of fall,

(ii) An electron moving with a constant velocity v along X-axis enters a uniform electric field applied along Y-axis. Then the electron moves.

(iii) Two equal and opposite charges of masses m_l and m₂ are accelerated in an uniform electric field through the same distance. What is the ratio of their accelerations if their ratio of masses is \(\frac{m_{1}}{m_{2}}=0.5 ?\)

(iv) A particle of mass m carrying charge q is kept at rest in a uniform electric field E and then released. The kinetic energy gained by the particle, when it moves through a distance y is

(v) A charged particle is free to move in an electric field. It will travel

In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force qE just equaled Mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of 1.6 x 10^-19 C the charge of the electron. For this, he won the Nobel prize.

(i) If a drop of mass 1.08 x 10^-14 kg remains stationary in an electric field of 1.68 x 10⁵ N C^-I, then the charge of this drop is

(ii) Extra electrons on this particular oil drop (given the presently known charge of the electron) are

(iii) A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field 100 V m^-1.If the mass of the drop is 1.6 X 10^-3 g, the number of electrons carried by the drop is (g= 10 m s^-2)

(iv) The important conclusion given by Millikan's experiment about the charge is

(v) If in Millikan's oil drop experiment, charges on drops are found to be \(8 \mu \mathrm{C}, 12 \mu \mathrm{C}, 20 \mu \mathrm{C}\) then quanta of charge is

In Pradeep's classroom, the fan was running very slowly. Due to which, his teacher was sweating and was restless and tired.All his classmates wanted to rectify this. They called an electrician who came and changed the capacitor only, after which the fan started running fast.
Answer the following questions based on the above information:
(i) What energy is stored in the capacitor and where?
(ii) A thin metal sheet is placed in the middle of a parallel plate capacitor. What will be the effect on the capacitance?
(iii) What values did the classmates have?

When an electric dipole of moment \(\left| P \right| \) = q \(\times\) 2a is held at an angle \(\theta\), with the direction of uniform external electric field E, a torque \(\tau \) = pE sin\(\theta\) acts on the dipole. This torque tries to align the electric dipole in the direction of the field. When p is along E, \(\theta=0^{o}\), \(\tau \) = pE sin\(0^{o}\) = zero.

Read the above passage and answer the following questions. 
(i) What is the direction of torque acting on an electric dipole held at a angle with uniform external field?
(ii) An electric dipole of length 10 cm having charge \(\pm 6\times { 10 }^{ -3 }\), C placed at \(30^{o}\) with respect to a uniform electric field experiences a torque of magnitude \(6\sqrt { 3 } \) N-m. Calculate magnitude of electric field.
(iii) What is the physical significance of this concept in our day-today life?

The surface integral of electrostatic field E produced by any source over any closed surface S enclosing a volume V in vacuum, i.e. total electric flux over the closed surface S in vacuum is \(1/{\epsilon}_{0}\) times the total charge Q contained inside S, i.e.
\({\phi}_{E}=\oint E.dS={{Q}\over{{\epsilon}_{0}}}\)
The charges inside S may be point charges or even continuous charge distributions. There is no contribution to "total electric flux from the charges outside S. Further, the location of Q inside S does not affect the value of surface integral.
Read the above passage and answer the following questions
What are the SI units and dimensions of electric flux?
A closed surface in vacuum encloses charges -q, + 3q and +5q. Another charge + 4q lies outside the surface. What is total electric flux over the surface?
A point charge a lies inside a spherical surface of radius r. How will the electric flux be affected, if, radius of the sphere is doubled?
What values of life do you learn from this theorem?

Vishwajeet purchased cells for his transistor. He felt that cells are not working properly. He wanted to check their emf. So, he took the cells to the physics lab and with the help of potentiometer found their emf. To his surprise, emf was less than the value claimed by the manufacturer. He lodged the complaint with consumer forum and received the deserving response.
Read the above passage and answer the following question.
(i) What values are displayed by Vishwajeet?
(ii) Why do you think Vishwajeet used potentiometer instead of voltmeter to find out emf of the cell? For more precise measurement, the potential gradient of the potentiometer should be high or low?

Saniya and Priya are friends. Both of them know that a small compass needle point always along north-south direction. One day Saniya is plotting field due to a bar magnet in the laboratory. She discovers a point where compass needle does not point along N-S. Rather, it sets itself in any arbitrary direction. Saniya thinks first that compass needle has become faulty. Priya then explains to her the real situation.
Read the above passage and answer the following questions:
(i) How did Priya justify the situation?
(ii) If a bar magnet is placed along the N-S direction with its north pole pointing north, what is the position of neutral points?
(iii) If a bar magnet is placed along N-S direction with its north pole pointing South, What is the position of neutral points?
(iv) What values of life do you learn from this piece of knowledge?

A rectangular coil of n turns each of area A, carrying current I, when suspended in a uniform magnetic field B, experiences a torque
\(\tau =nI \ BA \ sin\theta \)
Where is \(\theta \) the angle which a normal drawn on the plane of coil makes with the direction of magnetic field. This torque tends to rotate the coil and bring it in an equilibrium position. In the stable equilibrium state, the resultant force on the coil is zero. The torque on the coil is also zero and the coil has minimum potential energy.
Read the above passage and answer the following questions:
(i) In which position, a current carrying coil suspended in uniform magnetic field experiences
(a) minimum torque and
(b) maximum torque?
(ii) a circular coil of 200 turns, radius 5 cm carries a current of 2.0 A. It is suspended vertically in a uniform horizontal magnetic field of 0.20 T, with the plane of the coil making an angle with \(60°\) the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning.
(iii) what is the basic value displayed by the above study?

That night Vaikunth was preparing for his physics exam. Suddenly, the light in his room went off and he could not continue his studies. His cousin brother Vasu who had come to visit him was quick to react. Vasu using the torch (an android application) installed in his mobile phone found that the fuse had blown out. He checked the wiring and located a short circuit. He checked the wiring and located a short circuit. He rectified it and put a fuse wire. The light came to life again. Vaikunth had a sign of releif and continued his studies.
Read the above passage and answer the following question.
(i) What are the values projected by Vaikunth and Vasu?
(ii) Why did Vasu have to check the wiring?
(iii) What is an electric fuse? What characteristics you would prefer for a fuse wire?

Two linear parallel conductors carrying currents in the same direction attract each other and two linear parallel conductors carrying in opposite directions repel each other. The force acting per unit length due to currents \({ I }_{ 1 }and{ I }_{ 2 }\)in two linear parallel conductors held distance r apart in vacuum in SI unit is \(F=\frac { { \mu }_{ 0 } }{ 2\pi } \frac { 2{ I }_{ 1 }{ I }_{ 2 } }{ r } \)
Read the above passage and answer the following questions:
(i) What is the basic reason for the force between two linear parallel conductors currents?
(ii) Two straight wires A and B of lengths 2 cm and 20 cm, carrying currents  2.0 A and 5.0 A respectively in opposite directions are lying parallel to each other 4.0 cm apart. The wire A is held near the middle of wire B. What is the force on 20 cm long wire B?
(iii) What does this study imply in day to day life? 

Self- inductance is the property of a coil by virtue of which the coil oppose any change in the strength of current flowing through it by inducing an emf in itself. The induced emf is also called back emf. Self-inductance represents electric inertia which is measured in terms of coefficient of self-inductance(L). We can show that
L =  \(L=\cfrac { \phi }{ I } \) = \(\cfrac { -e }{ { \triangle I }/{ \triangle t } } \) 
Read the above passage and answer the following questions:
(i) How does the self-inductance of a coil represent its electric inertia?
(ii) An emf of 100\(\mu\) V is induced in a coil when the current in it changes from 5A to 1A in 0.4s.
Find the self-inductance of the coil.

Raj is in XII standard. His Physics teacher demonstrated an experiment to explain Faraday's laws of electromagnetic induction. Raj interrupted his lecture and asked, "Is there any possibility of induced emf due to the earth's magnetism"? The teacher was stunned for a moment and gave this question for group discussion. Finally, the students came out with correct answer.
(i) Write the values that you learnt from this incident.
(ii) What can be reason for Raj's question?

Equal currents I = 2A are flowing through the infinitely long wires parallel to Y-axis located at x = +1m, x = +2m, x = +4m and so on, but in opposite directions as shown in figure. Find the magnetic field at the origin O.

One alpha particle and a deuteron entered perpendicularly in a uniform magnetic field with same velocity. Which one follow the greater circle?

A charge particle moving in a magnetic field penetrates a layer of lead and thereby losses half of its kinetic energy. How does the radius of curvature of its path change?

You are given a copper wire carrying current I of length L. Now the wire is turned into circular coil. Find the number of turns in the coil so that the torque at the centre of the coil is to maximum

when is more power delivered to a light bulb, just after it is turned on and the glow of the filament is increasing or after it has been ON for a few seconds and the glow is steady?

A cell of emf E and internal resistance r is connected across a variabl resistor R. Plot a graph showing variation terminal voltage V of the cell versus the current I. Using the plot, show how emf of the cell and its internal resistance can be determined.

Use Kirchhoff's rules to determine the potential difference between the points A and D. When no current flows in the arm BE of the electric network shown in the figure below.
    

AB is a potentiometer wire as shown in figure. If the value of R is increased, in which direction will the balance point J shift?

Three resistance 3Ω, 6Ω and 9Ω are connected to a battery. In which of them will the power dissipation be maximum if
a) They are all connected in parallel
b) They are all connected in series Give reason.

For faster action which transistor is used and why?

A germanium diode is preferred to a silicon one for rectifying small voltages. Explain why?

Express by a truth table the output Y for all possible inputs A and B in the circuit shown below 

Write the Boolean equation and truth table for the circuit shown below.What is the output when all the inputs are high?

Construct AND gate using NAND GATE and give its truth table

In the working of a transistor, emitter-base junction is forward biased while collector-base junction is reverse biased. Why?

In normal case, emitter-base junction is the forward bias and collector-base junction is reverse biased. What will happen if emitter is reverse biased and collector is forward biased?

Two car generates have a common gate which needs to open automatically when a car enters either of the garages or cars enter both. A circuit, that resembles this situation using diodes for this situation.

A Zener of power rating 1 W is to be used as a voltage regulator. If Zener has a breakdown of 5 V and it has to regulate voltage which fluctuated between 3 V and 7 V, what should be the value of R_S for safe operations as shown below figure?
   

Give a brief explanation that how a NOT gate is realised Using NAND gate.

An onject AB is kept in front of a concave mirror as shown in the figure.
   
Complete the ray diagram showing the image formation of the object.

When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons.
(i) Is the frequency of reflected and refracted light same as the frequency of incident light?
(ii) Does the decrease in speed imply a reduction in the energy carried light wave?

In the given figure, for what value of (For prism, \(\mu\)=1.524

Two convex lenses of same focal but of aperture lenses in twp astronomical telescope having the identical eyepeice. What is the ratio of their resolving power? Which telescope will you prefer and why? Give reason.

Find an expression for intensity of transmitted light, when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will thw transmitted intensity be maximum?

Can we increase the range of a telescope by increasing the diameter of the objective lens?

A man stands in front of a mirror of special shape. He finds that his image has a very small head, a fat body and legs of normal size. What can you say about the shapes of three parts of the mirror? 

For the same angle of incidence, the angles of refraction in media P, Q and R are \(35°,25°,15°\) resp. In which medium will the velocity of light be minimum? 

A lens whose radii of curvature are different is forming the image of an object placed on its axis. If the lens is reversed, will the position of the image change? 

Is Huygen's principle valid for longitundinal sound waves?

A square surface of side l metre is in the plane of paper. A uniform electric field E (volt/metre), also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). What is the electric flux associated with this surface?

A thin fixed ring of radius 2 m has a positive charge of 10^-6C uniformly distributed over it. A particle of mass 0.9 g and having a negative charge 10^-7C is placed on the axis at a distance of 2cm from the center of the ring. Show that motion of the negatively charged particle is approximately SHM. Calculate the time period of oscillation.

A charged Particle q is shot towards another charged particle Q which is fixed , with a speed v. It approaches Q up to a closet distance r and then returns, If q were given a speed 2 v the n find the closet distance of approach.

Two Capacitors of capacitace 6\(\mu \)F and 12\(\mu \)F ae connnected in series with tha battery the volatage across the 6\(\mu \)F capacitor is 2 volt, Compute the total battery voltage.

An electric dipole is held in an uniform electric field. Using suitable diagram, show at it doesn't undergo any translatory motion, and (ii) derive an expression for torque acting on it and specify its direction.

A charged Particle is free to move in an electric field. Will it always move along an electric line of force ?

A 2m insulating slab with a large aluminum sheet of area 1m² on its top is fixed by a man outside his house one evening. Will he get an electric shock, if he touches the metal sheet next morning?

Guess a possible reason, why water has a much greater dielectric constant (= 80) than mica (= 6)?

A technician has only two capacitors. By using them in series or in parallel, he is able to obtain the capacitance of 4 \(\mu \) F, 5 \(\mu \) F, 20  \(\mu \) F. and 25 \(\mu \) F. What is the capacitance of both capacitors?

A and B have identical size and same mass. A becomes A²⁺ and B become B^2- . Will A²⁺ and B^2- still have the same mass? Why?

A schematic arrangement for transmitting a message signal (20 Hz to 20kHz) is given below:

Give two drawbacks from which this arrangement suffers. Describe briefly with the help of a block diagram the alternative arrangement for the transmission and reception of the message signal

The TV transmission tower at a particular place has a height of 160m. What is its coverage range? By how much should the height be increased to double its coverage range? Given that radius of earth = 6400 km

A TV tower has a height of 110m. How much population is covered by the TV broadcast if the average population density around the tower is 1000 km^-2? Given that radius of Earth = 6.4 x 10⁶m

A microwave telephone link operating at the cenral frequency of 10 GHz has been established .If 2 % of this is available for microwave communication channel, then how many telephones channels can be simultaneously granted if each telephone is allotted a band width of 8 KHz

You are given three semiconductors A,B,C with respective band gaps of 3eV, 2eV and 1eV for use in a photodetector to detect \(\lambda \) = 1400nm . Select the suitable semiconductor. Give reasons

How are side bands produced?

Why are microwave considered better carriers of signals than ratio waves?

In the given diagram C(t) stands for the carrier wave and m(t) for the signal to be transmitted. What name do we give to the wave labelled as C_m(t) in the diagram?

The carrier wave is given by   C(t) = 2 sin \((8\pi t)\) volt. The modulating signal is a square wave as shown. Find modulation index.

Why are micro wave used in radars?

The earth's magnetic field at a point on its surface is usually characterised by three quantities: (a) declination (b) inclination or dip and (c) horizontal component of the field. These are known as the elements of the earth's magnetic field. At a place, angle between geographic meridian and magnetic meridian is defined as magnetic declination, whereas angle made by the earth's magnetic field with the horizontal in magnetic meridian is known as magnetic dip.

(i) In a certain place, the horizontal component of magnetic field is \(\frac{1}{\sqrt{3}}\) times the vertical component. The angle of dip at this place is 

(ii) The angle between the true geographic north and the north shown by a compass needle is called as

(iii) The angles of dip at the poles and the equator respectively are

(iv) A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It

(v) Select the correct statement from the following

By analogy to Gauss's law of electrostatics, we can write Gauss's law of magnetism as \(\oint \vec{B} \cdot d \vec{s}=\mu_{0} m_{\text {inside }}\) where \(\oint \vec{B} \cdot d \vec{s}\) is the magnetic flux and \(m_{\text {inside }}\) is the net pole strength inside the closed surface.
We do not have an isolated magnetic pole in nature. At least none has been found to exist till date. The smallest unit of the source of magnetic field is a magnetic dipole where the net magnetic pole is zero. Hence, the net magnetic pole enclosed by any closed surface is always zero. Correspondingly, the flux of the magnetic field through any closed surface is zero.

(I) Consider the two idealised systems
(i) a parallel plate capacitor with large plates and small separation and
(ii) a long solenoid oflength L >> R, radius of cross-section.
In (i) \(\vec{E}\) is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zerq outside. These idealised assumptions, however, contradict fundamental laws as below

(ii) The net magnetic flux through any closed surface, kept in a magnetic field is

(iii) A closed surface S encloses a magnetic dipole of magnetic moment 2ml. The magnetic flux emerging from the surface is

(iv) Which of the following is not a consequence of Gauss's law?

(v) The surface integral of a magnetic field over a surface

When the atomic dipoles are aligned partially or fully, there is a net magnetic moment in the direction of the field in any small volume of the material. The actual magnetic field inside material placed in magnetic field is the sum of the applied magnetic field and the magnetic field due to magnetisation. This field is called magnetic intensity (H).
\(H=\frac{B}{\mu_{0}}-M\)
where M is the magnetisation of the material, llo is the permittivity of vacuum and B is the total magnetic field. The measure that tells us how a magnetic material responds to an external field is given by a dimensionless quantity is appropriately called the magnetic susceptibility: for a certain class of magnetic materials, intensity of magnetisation is directly proportional to the magnetic intensity.
(i) Magnetization of a sample is

(ii) Identify the wrongly matched quantity and unit pair.

(iii) A bar magnet has length- 3 cm, cross-sectional area 2 cm² and magnetic moment 3 A m². The intensity of magnetisation of bar magnet is

(iv) A solenoid has core of a material with relative permeability 500 and its windings carry a current of 1 A. The number of turns of the solenoid is 500 per metre. The magnetization of the material is nearly

(v) The relative permeability of iron is 6000. Its magnetic susceptibility is

The magnetic field lines of the earth resemble that of a hypothetical magnetic dipole located at the centre of the earth. The axis of the dipole is presently tilted by approximately 11.3^o with respect to the axis of rotation of the earth.

The pole near the geographic North pole of the earth is called the North magnetic pole and the pole near the geographic South pole is called South magnetic pole.
(i) The strength of the earth's magnetic field varies from place to place on the earth's surface, its value being of the order of

(ii) A bar magnet is placed North-South with its North-pole due North. The points of zero magnetic field will be in which direction from centre of magnet?

(iii) The value of angle of dip is zero at the magnetic equator because on it

(iv) The angle of dip at a certain place, where the horizontal and vertical components of the earth's magnetic field are equal, is

(v) At a place, angle of dip is 30°. If horizontal component of earth's magnetic field is H, then the total intensity of magnetic field will be

The field of a hollow wire with constant current is homageneous
Curves in the graph shown give, as functions of radius distance r, the magnitude B of the magnetic field inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels.

(i) Which wire has the greatest magnitude of the magnetic field on the surface?

(ii) The current density in a wire a is

(iii) Which wire has the greatest radius?

(iv) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

(v) In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite direction. The magnetic field is zero

Ampere's law gives a method to calculate the magnetic field due to given current distribution. According to it, the circulation \(\oint \vec{B} \cdot d \vec{l}\) of the resultant magnetic field along a closed plane curve is equal to \(\mu_{0}\) times the total current crossing the area bounded by the closed curve provided the electric field inside the loop remains constant. Ampere's law is more useful under certain symmetrical conditions. Consider one such case of a long Straight wire with circular cross-section (radius R) carrying current I uniformly distributed across this cross-section.

(i) The magnetic field at a radial distance r from the centre of the wire in the region r > R, is