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
Correct Answer: $$\rho \left( {\overrightarrow {\bf{r}} ,\,t} \right) = \rho \left( {\overrightarrow {\bf{r}} ,\,0} \right)\exp \left( { - \frac{{\sigma t}}{\varepsilon }} \right)$$