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 = 1029 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 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
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