Match List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Gauss's Law in Electrostatics	$I$. $\oint \vec{E} \cdot d \vec{l} = -\frac{d \phi_B}{d t}$
$B$. Faraday's Law	$II$. $\oint \vec{B} \cdot d \vec{A} = 0$
$C$. Gauss's Law in Magnetism	$III$. $\oint \vec{B} \cdot d \vec{l} = \mu_0 i_C + \mu_0 \epsilon_0 \frac{d \phi_E}{d t}$
$D$. Ampere-Maxwell Law	$IV$. $\oint \vec{E} \cdot d \vec{s} = \frac{q}{\epsilon_0}$

Choose the correct answer from the options given below:

$A$ long straight cable of length $l$ is placed symmetrically along $z-$ axis and has radius $a (a << l)$. The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I(t) = I_0 \sin(2\pi \nu t)$ flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance $s$ from the wire inside the cable is $\vec{E}(s,t) = \mu_0 I_0 \nu \cos(2\pi \nu t) \ln(s/a) \hat{k}$.
$(i)$ Calculate the displacement current density inside the cable.
$(ii)$ Integrate the displacement current density across the cross-section of the cable to find the total displacement current $I_d$.
$(iii)$ Compare the conduction current $I_0$ with the displacement current $I_d$.

The charge on a capacitor varies with time as $q = q_0 \sin(2\pi nt)$. What is the displacement current produced in the dielectric of the capacitor?

The electric field through an area of $2 \ m^2$ varies with time as shown in the graph. The greatest displacement current through the area is at $t = ..... \ \mu s$.

Which of the following produces electromagnetic waves?

The voltage between the plates of a parallel plate capacitor of capacity $1 \ \mu F$ is changing at the rate of $4 \ V/s$. The displacement current in the capacitor is: (in $\mu A$)