At time t = 0, a charge distribution $$\rho \left( {\overrightarrow {\bf{r}} ,\,0} \right)$$ exists within an ideal homogeneous conductor of permittivity $$\varepsilon $$ and conductivity $$\sigma $$. At a later time $$\rho \left( {\overrightarrow {\bf{r}} ,\,t} \right)$$ is given by
A. $$\rho \left( {\overrightarrow {\bf{r}} ,\,t} \right) = \rho \left( {\overrightarrow {\bf{r}} ,\,0} \right)\exp \left( { - \frac{{\sigma t}}{\varepsilon }} \right)$$
B. $$\rho \left( {\overrightarrow {\bf{r}} ,\,t} \right) = \frac{{\rho \left( {\overrightarrow {\bf{r}} ,\,0} \right)}}{{1 + {{\left( {\frac{{\sigma t}}{\varepsilon }} \right)}^2}}}$$
C. $$\rho \left( {\overrightarrow {\bf{r}} ,\,t} \right) = \rho \left( {\overrightarrow {\bf{r}} ,\,0} \right)\exp \left[ { - {{\left( {\frac{{\sigma t}}{\varepsilon }} \right)}^2}} \right]$$
D. $$\rho \left( {\overrightarrow {\bf{r}} ,\,t} \right) = \rho \left( {\overrightarrow {\bf{r}} ,\,0} \right)\exp \frac{\varepsilon }{{\sigma t}}\sin \left( {\frac{{\sigma t}}{\varepsilon }} \right)$$
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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