Four charges are arranged at the corners of the square PQRS of side an as shown in the figure.
(a) Find the work required to assemble these charges in the given configuration.
(b) Suppose a charge q is brought to the center of the square, by keeping the four charges fixed at the corners, how much extra work is required for this?

A parallel plate capacitor has square plates of side 5 cm and separated by a distance of 1 mm.
(a) Calculate the capacitance of this capacitor.
(b) If a 10 V battery is connected to the capacitor, what is the charge stored in any one of the plates? (The value of ε_o = 8.85 x 10^-12 Nm² C^-2)

Draw the free body diagram for the following charges as shown in the figure (a), (b) and (c).

Calculate the resultant capacitances for each of the following combinations of capacitors.

Two electric bulbs marked 20 W – 220 V and 100 W – 220 V are connected in series to 440 V supply. Which bulb will get fused?

The following figure shows a complex network of conductors which can be divided into two closed loops like EACE and ABCA. Apply Kirchoff’s voltage rule(KVR)

The resistance of a nichrome wire at 20^oC is 10 Ω. If its temperature coefficient of resistanc is 0.004^oC, find its resistance of the wire at boiling point of water. Comment on the result.

Two cells each of 5V are connected in series with a 8 Ω resistor and three parallel resistors of 4 Ω, 6 Ω, and 12 Ω. Draw a circuit diagram for the above arrangement. Calculate
(i) the current drawn from the cells
(ii) current through each resistor

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).

A bar magnet is placed in a uniform magnetic field whose strength is 0.8 T. If the bar magnet is oriented at an angle 30^o with the external field experiences a torque of 0.2 Nm. Calculate
(i) the magnetic moment of the magnet
(ii) the work done by the applied force in moving it from most stable configuration to the most unstable configuration and also compute the work done by the applied magnetic field in this case.

A capacitor of capacitance \(\frac { { 10 }^{ -4 } }{ \pi } F\), an inductor of inductance \(\frac { 2 }{ \pi } H\) and a resistor of resistance 100 Ω are connected to form a series RLC circuit. When an AC supply of 220 V, 50 Hz is applied to the circuit, determine
(i) the impedance of the circuit
(ii) the peak value of current flowing in the circuit
(iii) the power factor of the circuit and
(iv) the power factor of the circuit at resonance.

Determine the self-inductance of 4000 turn air-core solenoid of length 2m and diameter 0.04 m.

Calculate the instantaneous value at 60^o, average value and RMS value of an alternating current whose peak value is 20 A.

Consider a parallel plate capacitor whose plates are closely spaced. Let R be the radius of the plates and the current in the wire connected to the plates is 5 A, calculate the displacement current through the surface passing between the plates by directly calculating the rate of change of flux of electric field through the surface.

In Young's double-slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two-wavelength λ₀ = 750 nm and λ = 900mm. What is the minimum distance from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a . bright fringe from the other?

Find the minimum thickness of a film of refractive index 1.25, which will strongly reflect the light of wavelength 589 nm. Also find the minimum thickness of the film to be anti-reflecting.

Two polaroids are kept crossed (transmission axes at 90^o ) to each other.
(a) What will be the intensity of the light coming out from the second polaroid when an unpolarised light of intensity I falls on the first polaroid?
(b) What will be the intensity of light coming out from the second polaroid if a third polaroid is kept in between at 45^o inclination to both of them.

Calculate the power of the lens of the spectacles needed to rectify the defect of nearsightedness for a person who could see clearly up to a distance of 1.8 m.

At the given point of time, the earth receives energy from sun at 4 cal cm^–2min^–1. Determine the number of photons received on the surface of the Earth per cm² per minute. (Given: Mean wavelength of sun light = 5500 Å )

Consider two hydrogen atoms H_A and H_B in ground state. Assume that hydrogen atom H_A is at rest and hydrogen atom H_B is moving with a speed and make head-on collision with the stationary hydrogen atom H_A. After the collision, both of them move together. What is minimum value of the kinetic energy of the moving hydrogen atom H_B, such that any one of the hydrogen atoms reaches first excitation state.

Characol pieces of tree is found from an archeological site. The carbon-14 content of this characol is only 17.5% that of equivalent sample of carbon from a living tree. What is the age of tree?

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.

Prove the Boolean identity AC + ABC = AC and give its circuit description.