An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma = 10 \,\mathrm{mho} / \mathrm{m}$. The ratio of maximum conduction current density to maximum displacement current density is $\_\_\_\_$.

$$ \left[\text { Take } \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\, \mathrm{Nm}^2 / \mathrm{C}^2\right] $$

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5 \mu \mathrm{~F}$. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _________ $\mathrm{Vs}^{-1}$.

A parallel plate capacitor of area $A=16 \mathrm{~cm}^2$ and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area $\mathrm{A}_0=3.2 \mathrm{~cm}^2$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $\mathrm{A}_0$ is __________ mA .

In a medium the speed of light wave decreases to $$0.2$$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $$x: 1$$. The value of $$x$$ is _________.

(Given speed of light in free space $$=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$$ and for the given medium $$\mu_{\mathrm{r}}=1$$)