The electric field E(r, t) at a point r at time t in a metal due to the passage of electrons can be described by the equation $${\nabla ^2}\overrightarrow {\bf{E}} \left( {\overrightarrow {\bf{r}} ,\,t} \right) = \frac{1}{{{c^2}}}\left[ {\frac{{{\partial ^2}\overrightarrow {\bf{E}} \left( {\overrightarrow {\bf{r}} ,\,t} \right)}}{{\partial {t^2}}} + \omega {'^2}\overrightarrow {\bf{E}} \left( {\overrightarrow {\bf{r}} ,\,t} \right)} \right]$$
where, $$\omega '$$ is a characteristic associated with the metal and c is the speed of light in vacuum. The dispersion relation corresponding to the plane wave solutions of the form exp $$\left[ {i\left( {\overrightarrow {\bf{i}} .\overrightarrow {\bf{r}} - \omega t} \right)} \right]$$ is given by
A. $${\omega ^2} = {c^2}{k^2} - \omega {'^2}$$
B. $${\omega ^2} = {c^2}{k^2} + \omega {'^2}$$
C. $$\omega = ck - \omega '$$
D. $$\omega = ck + \omega '$$
Answer: Option A
This Question Belongs to Engineering Physics >> Electromagnetic Theory
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. 0.033 μm
B. 0.330 μm
C. 3.300 μm
D. 33.000 μm
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. $$ - {\bf{\hat z}}k$$
A. vp = vg
B. vp = $${\text{v}}_{\text{g}}^{\frac{1}{2}}$$
C. vp vg = c2
D. vg = $${\text{v}}_{\text{p}}^{\frac{1}{2}}$$
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