Calculate displacement current through half of the area of a capacitor of area $\mathrm{A}$ and separation between plates $\mathrm{d}$ charged by constant current $\mathrm{I}$.

A parallel plate capacitor has two circular plates of radius $R$ each, separated by a distance $d$. The magnitude of the instantaneous electric field between the plates is given by $E=E_0\sin \omega t$, where $E_0$ and $\omega$ are positive constants. A positive value of $E$ corresponds to the upward direction as shown in the figure.

At $t=0$, the displacement current between the plates is

What is displacement current? Give the expression for it.

A long wire of radius $R$ is made of two different metals, depositing one metal over the other. The inner core occupies the region $r<R$ and the outer region $R<r\le 2R$. Because of difference in the conductivity of the two wires, only $10\%$of the total current flows through the inner core and the balance through the second metal. The current density in each metal is constant.

The magnetic field at a distance $r=\frac{3R}{2}$ from the centre is

A plain EM wave moving with a velocity $3\times {10}^8{\mathrm{ms}}^{-1}$has an electric field which oscillates sinusoidally with a frequency $2\times {10}^{12 }\mathrm{Hz}$ and amplitude $48 \mathrm{V}/\mathrm{m}$. What is the amplitude of the oscillating magnetic field?

Match List I and List II

Choose the correct answer from the options given below :

Seawater at a frequency $f=9\times {10}^2 \mathrm{Hz}$, has permittivity $\epsilon =80{\epsilon }_0$ and resistivity $\rho =0.25 \mathrm{\Omega } \mathrm{m}$. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source $V\left(t\right)=V_0\sin \left(2\pi ft\right)$. Then the conduction current density becomes ${10}^{\mathrm{x}}$ times the displacement current density after time $t=\frac{1}{800} \mathrm{s}.$ The value of $x$ is _______

(Given $\left.:\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}\right)$