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 $$\mu_{\mathrm{r}}=1$$)

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of $$24 \mathrm{~W}$$. The radius of curvature of hemisphere is $$10 \mathrm{~cm}$$ and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ____________ $$\times~10^{-8} \mathrm{~N}$$.