The displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu F$ is $150 \mu A$. The capacitor is charged by a source of varying potential at the rate of: (in $Vs^{-1}$)

Electromagnetic waves can be produced by . . . . . . .

Match List-$I$ with List-$II$ and choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $A$. Gauss's law of magnetostatics | $I$. $\oint \vec{E} \cdot d\vec{a} = \frac{1}{\epsilon_0} \int \rho dV$ |
| $B$. Faraday's law of electromagnetic induction | $II$. $\oint \vec{B} \cdot d\vec{a} = 0$ |
| $C$. Ampere's law | $III$. $\oint \vec{E} \cdot d\vec{l} = -\frac{d}{dt} \int \vec{B} \cdot d\vec{a}$ |
| $D$. Gauss's law of electrostatics | $IV$. $\oint \vec{B} \cdot d\vec{l} = \mu_0 I$ |

The charge on a parallel plate capacitor varies as $q = q_0 \cos(2\pi \nu t)$. The plates are very large and close together (area $= A$,separation $= d$). Neglecting the edge effects,find the displacement current through the capacitor.

$AC$ voltage $V(t) = 20 \sin \omega t$ of frequency $50 \, Hz$ is applied to a parallel plate capacitor. The separation between the plates is $2 \, mm$ and the area is $1 \, m^2$. The amplitude of the oscillating displacement current for the applied $AC$ voltage is ...... $\mu A$.
[Take $\varepsilon_0 = 8.85 \times 10^{-12} \, F/m$]

$A$ parallel plate capacitor of area $60\, cm^2$ and separation $3\, mm$ is charged initially to $90\, \mu C$. If the medium between the plates becomes slightly conducting and the plate loses the charge at the rate of $2.5\times10^{-8}\, C/s$,what is the magnetic field between the plates?