Consider two point charges q₁ and q₂ at rest as shown in the figure.

They are separated by a distance of 1m. Calculate the force experienced by the two charges for the following cases:
(a) q₁ = +2μC and q₂ = +3μC
(b) q₁ = +2μC and q₂ = -3μC
(c) q₁= +2μC and q₂ = -3μC kept in water (ε_r = 80)

A spark plug in a bike or a car is used to ignite the air-fuel mixture in the engine. It consists of two electrodes separated by a gap of around 0.6 mm gap as shown in the figure.

To create the spark, an electric field of magnitude 3 x 10⁶ Vm^-1 is required.
(a) What potential difference must be applied to produce the spark?
(b) If the gap is increased, does the potential difference increase, decrease or remains the same?
(c) find the potential difference if the gap is 1 mm.

A battery of voltage V is connected to 30 W bulb and 60 W bulb as shown in the figure.
(a) Identify brightest bulb
(b) which bulb has greater resistance?
(c) Suppose the two bulbs are connected in series, which bulb will glow brighter?

Three identical lamps each having a resistance R are connected to the battery of emf ε as shown in the figure.

Suddenly the switch S is closed.
(a) Calculate the current in the circuit when S is open and closed
(b) What happens to the intensities of the bulbs A, B, and C.
(c) Calculate the voltage across the three bulbs when S is open and closed
(d) Calculate the power delivered to the circuit when S is opened and closed
(e) Does the power delivered to the circuit decrease, increase or remain same?

A proton moves in a uniform magnetic field of strength 0.500 T magnetic field is directed along the x - axis. At initial time, t  = 0s, the proton has velocity
\(\hat { v } =(1.95\times { 10 }^{ -5 }\hat { i } +2.00\times { 10 }^{ 5 }\hat { k } )m{ s }^{ -1 }\). Find
(a) At initial time, what is the acceleration of the proton.
(b) Is the path circular or helical? If helical, calculate the radius of helical trajectory and also calculate the pitch of the helix (Note: Pitch of the helix is the distance travelled along the helix axis per revolution).

Calculate the magnetic field at the centre of a square loop which carries a current of 1.5 A, length of each side being 50 cm.

A circular loop of area 5 x 10^–2 m² rotates in a uniform magnetic field of 0.2T. If the loop rotates about its diameter which is perpendicular to the magnetic field as shown in figure. Find the magnetic flux linked with the loop when its plane is
(i) normal to the field
(ii) inclined 60^o to the field and
(iii) parallel to the field.

A 500 μH inductor, \(\\ \frac { 80 }{ { \pi }^{ 2 } } pF\) capacitor and a 628 Ω resistor are connected to form a series RLC circuit. Calculate the resonant frequency and Q-factor of this circuit at resonance.

Write short notes on
(a) microwaves
(b) X - rays
(c) Radio waves
(d) Visible spectrum

Give two uses each of
(i) IR radiation,
(ii) Microwaves and
(iii) UV radiation.

A compound microscope has a magnification of 30. The focal length of eye piece is 5 cm Assuming the final image to be at least distance of distinct vision, find the magnification produced by the objective.

Find the position of the image of a point object O in the two cases given. Take the radius of curvature of the surface R as 15 cm, n₁ = 1 and n₂ = 2.
Case i) O is located 10 cm to the left of the surface.
Case ii) O is located 30 cm to the left of the surface.

When a 6000Å light falls on the cathode of a photo cell, photoemission takes place. If a potential of 0.8 V is required to stop emission of electron, then determine the
(i) frequency of the light
(ii) energy of the incident photon
(iii) work function of the cathode material
(iv) threshold frequency and
(v) net energy of the electron after it leaves the surface.

Calculate the momentum and the de Broglie wavelength in the following cases:
i) an electron with kinetic energy 2 eV.
ii) a bullet of 50 g fired from rifle with a speed of 200 m/s
iii) a 4000 kg car moving along the highways at 50 m/s
Hence show that the wave nature of matter is important at the atomic level but is not really relevant at macroscopic level.

On your birthday, you measure the activity of the sample ²¹⁰Bi which has a half-life of 5.01 days. The initial activity that you measure is 1µCi.
(a) What is the approximate activity of the sample on your next birthday? Calculate
(b) the decay constant
(c) the mean life
(d) initial number of atoms.

(a) Calculate the disintegration energy when stationary \(_{ 92 }^{ 232 }{ U }\)  nucleus decays to thorium \(_{ 90 }^{ 228 }{ Th }\)  with the emission of α particle. The atomic masses are of  \(_{ 92 }^{ 232 }{ U }\) = 232.037156 u, \(_{ 90 }^{ 228 }{ Th }\) = 228.028741u and \(_{ 2 }^{ 4 }{ He }\) = 4.002603 u
(b) Calculate kinetic energies of \(_{ 90 }^{ 228 }{ Th }\) and α-particle and their ratio.

What is the difference between Nano materials and Bulk materials?

Elaborate any two types of Robots with relevant examples.

What are polariser and analyser?

A monochromatic light of wavelength 5000  Å passes through a single slit producing diffraction pattern for the central maximum as shown in the figure. Determine the width of the slit.

Four silicon diodes and a 10 Ω resistor are connected as shown in figure below. Each diode has a resistance of 1Ω. Find the current flows through the 10Ω resistor.

The output characteristics of a transistor connected in common emitter mode is shown in the figure. Determine the value of IC when V_CE = 15 V. Also determine the value of I_C when V_CE is changed to 10 V

Define and derive an expression for the energy density in parallel plate capacitor.

The mass of an electron in hydrogen atom is 9.1 x 10^-31 Kg. It revolves around the nucleus in a circular orbit of radius 0.53 \(\stackrel {o} A\) calculate its angular velocity [e = 1.6 x 10^-19C]

Derive a relation between internal resisance and emf of a cell.

State seebeck effect and give two applications.

Calculate the magnetic field at a point P which is perpendicular bisector to current carrying straight wire as shown in figure.

Can a galvanometer be used for measuring the current? Explain.

State the principle of a Transformers.

The frequency of a ratio station is in the range from 7.5 MHz to 12 MHz band. Calculate the corresponding wavelength band.