The equation of the electric field of an electromagnetic wave propagating through free space is given by : $E=\sqrt{377} \sin \left(6.27 \times 10^3 t-2.09 \times 10^{-5} x\right) \mathrm{N} / \mathrm{C}$

The average power of the electromagnetic wave is $\left(\frac{1}{\alpha}\right) \mathrm{W} / \mathrm{m}^2$. The value of $\alpha$ is

$$ \left(\text { Take } \sqrt{\frac{\mu_0}{\varepsilon_o}}=377 \text { in SI units }\right) $$

The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by,

$$ E_{\mathrm{y}}=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} \mathrm{t}\right) \mathrm{V} / \mathrm{m} $$

(where $x, \mathrm{t}$ and other values have S.I. units). The dielectric constant of the medium is $\_\_\_\_$

(speed of light in free space is $3 \times 10^8 \mathrm{~m} / \mathrm{s}$ )

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 _________ $\mathrm{Vs}^{-1}$.