## Answer & Solution

**Option B**

1.

Which one of the following current densities, $$\overrightarrow {\bf{J}} $$ can generate the magnetic vector potential $$\overrightarrow {\bf{A}} = \left( {{y^2}{\bf{\hat i}} + {x^2}{\bf{\hat j}}} \right)?$$

2.

A metal has free-electron density n = 10^{29} m^{-3}. Which of the following wavelengths will excite plasma oscillations?

3.

The electric field of a plane electromagnetic wave is $$\overrightarrow {\bf{E}} = \overrightarrow {{{\bf{E}}_0}} \exp \left[ {i\left( {{\bf{\hat x}}k\cos \alpha + {\bf{\hat y}}k\sin \alpha - \omega t} \right)} \right].$$ If $${\bf{\hat x}},\,{\bf{\hat y}}$$ and $${{\bf{\hat z}}}$$ are cartesian unit vectors, the wave vector $$\overrightarrow {\bf{k}} $$ of the electromagnetic wave is

4.

The dispersion relation for a, low density plasma is ω^{2} = ω_{0}^{2} + c^{2} k^{2}, where ω_{0} is the plasma frequency and c is the speed of light in free space. The relationship between the group velocity (v_{g}) and phase velocity (v_{p}) is

5.

Aspherical conductor of radius a is placed in a uniform electric field $$\overrightarrow {\bf{E}} = {E_0}\,{\bf{\hat k}}.$$ The potential at a point P(r, θ) for r > a, is given by $$\phi \left( {r,\,\theta } \right) = {\text{constant}} - {E_0}r\cos \theta + \frac{{{E_0}{a^3}}}{{{r^2}}}\cos \theta $$

where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.

The charge density on the sphere at θ = 30° is

where, r is the distance of P from the centre O of the sphere and θ is the angle, OP makes with the Z-axis.

The charge density on the sphere at θ = 30° is

6.

A non-relativistic charged particle moves along the positive X-axis with a constant positive acceleration $$a{\bf{\hat x}}.$$ The particle is at the origin at t = 0. Radiation is observed at t = 0 at a distant point (0, d, 0) on the Y-axis. Which one of the following statements is correct?

7.

In a non-conducting medium characterized by ε = ε_{0}, μ = μ_{0} and conductivity σ = 0, the electric field (in V/m) is given by $$\overrightarrow {\bf{E}} = 20\sin \left[ {{{10}^8}t - kz} \right]{\bf{\hat j}}.$$ The magnetic field $$\overrightarrow {\bf{H}} $$ (in A/m), is given by

8.

An electromagnetic wave with $$\overrightarrow {\bf{E}} \left( {z,\,t} \right) = {E_0}\cos \left( {\omega t - kz} \right){\bf{\hat i}}$$ is travelling in free space and crosses a disc of radius 2 m placed perpendicular to the Z-axis. If E_{0} = 60 V/m, the average power in watt, crossing the disc along the Z-direction is

9.

A charged capacitor (C) is connected in series with an inductor (L). When the displacement current reduces to zero, the energy of the LC circuit is

10.

In an electromagnetic field, which one of the following remains invariant under Lorentz transformation?