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

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

A metal has free-electron density n = 10²⁹ m^-3. Which of the following wavelengths will excite plasma oscillations?

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 (v_g) and phase velocity (v_p) is