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

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

The dispersion relation for a, low density plasma is ω2 = ω02 + c2 k2, where ω0 is the plasma frequency and c is the speed of light in free space. The relationship between the group velocity (vg) and phase velocity (vp) is

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.
Electromagnetic Theory mcq question image
The charge density on the sphere at θ = 30° is

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?

In a non-conducting medium characterized by ε = ε0, μ = μ0 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

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 E0 = 60 V/m, the average power in watt, crossing the disc along the Z-direction is

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