Question 1.

a) Consider the figure given below. Charges q1, q2 and q3 are placed at A, B and C, respectively, and q1 = q2 = -q3 = 2μC. Determine the magnitude and the direction of the electric field at point P.

b) A 100 m long thread carries charges uniformly distributed along its length. An electron, 10 cm away from the centre of the thread along a line perpendicular to the thread experiences an attractive force of 2.7 × 10^-12N. Calculate the total charge on the thread.

c) What do you understand by electrostatic potential energy? Calculate the electrostatic potential energy for the system of charges shown below. Take q = 4µC and a = 2 cm.

Question 2. a) The capacitance of a parallel plate capacitor is increased by a factor of 5 when a dielectric material fills the space between its plates. What is the relative permitivity of the dielectric material? If this material is placed in between the plates of a cylindrical capacitor of outer and inner radii 12 cm and 10 cm respectively, calculate the capacitance per unit length of the cylindrical capacitor.

b) A glass of relative permittivity 4 is kept in an external electric field of magnitude 10² Vm^-1. Calculate the polarisation vector, molecular/atomic polarisability and the refractive index of the glass.

Question 3. a) A copper wire of diameter 1 mm and length 30 m is connected across a battery of 2V. Calculate the current density in the wire and drift velocity of the electrons. The resistivity of copper is 1.72 x 10^-8 Ωm and n = 8.0 x 10²⁸ electrons m^-3.

b) A 10 eV electron is circulating in a plane at right angles to a uniform magnetic field of 1.0 × 10^-4 T. Calculate the orbital radius of the electron, cyclotron frequency, period of revolution, and the direction of circular motion of the electron as viewed by an observer looking along the magnetic field.

c) How do we differentiate between diamagnetic and paramagnetic materials? Show that for diamagnetic atoms placed in an external magnetic field B, the change in dipole moment is opposite to the direction of B.

d) Establish the relation B = μ₀ (H + M) for a ferromagnetic material.

Question 4. a) An electric generator comprises a square wire loop of side 100 cm. The loop has 50 turns and is placed in a magnetic field of 0.5T. By what frequency should this loop be rotated in the magnetic field to produce an AC voltage of peak value 250 V?

b) Explain the physical significance of the Maxwell's equation ∇ x Β = μ₀ (J + ε₀.∂E/∂t)

Derive the wave equation for the z-component of the electric field of an electromagnetic wave.

c) A sinusoidal plane electromagnetic wave propagates from water (n_w =1.33) to glass (n_g = 1.5).

Calculate the reflection and transmission coefficients for this wave at the interface of the two media.

Show that when an electromagnetic wave enters from one dielectric medium to the other, its frequency remains unchanged.