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

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. $$\frac{2}{{{\mu _0}}}\left( {x{\bf{\hat i}} + y{\bf{\hat j}}} \right)$$

B. $$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} + {\bf{\hat J}}} \right)$$

C. $$ - \frac{2}{{{\mu _0}}}\left( {{\bf{\hat i}} - {\bf{\hat j}}} \right)$$

D. $$\frac{2}{{{\mu _0}}}\left( {x{\bf{\hat i}} - y{\bf{\hat j}}} \right)$$

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

A. 0.033 μm

B. 0.330 μm

C. 3.300 μm

D. 33.000 μm

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

A. $${\bf{\hat z}}k$$

B. $${\bf{\hat x}}k\sin \alpha + {\bf{\hat y}}k\cos \alpha $$

C. $${\bf{\hat x}}k\cos \alpha + {\bf{\hat y}}k\cos \alpha $$

D. $$ - {\bf{\hat z}}k$$

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

A. v_p = v_g

B. v_p = $${\text{v}}_{\text{g}}^{\frac{1}{2}}$$

C. v_p v_g = c²

D. v_g = $${\text{v}}_{\text{p}}^{\frac{1}{2}}$$