At what rate must the potential difference between the plates of a capacitor be changed to set up a displacement current of $1 \, A$ in a capacitor of $2 \, \mu F$?

If the rate of change of electric field across the plates of a parallel plate capacitor is $E$ and the displacement current is $I$,then the area of one plate of the capacitor is ($\varepsilon_{0}$ is permittivity of free space).

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 | $IV$. $\oint \vec{B} \cdot d\vec{l} = \mu_0 I$ |

Match List-$I$ with List-$II$ and choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $A. \oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$ | $I. \text{Gauss' law for electricity}$ |
| $B. \oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$ | $II. \text{Gauss' law for magnetism}$ |
| $C. \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$ | $III. \text{Faraday law}$ |
| $D. \oint \vec{B} \cdot d\vec{A} = 0$ | $IV. \text{Ampere-Maxwell law}$ |

$A$ parallel-plate capacitor with circular plates is being discharged. The radius of the circular plates is $10 \ cm$. $A$ circular loop of radius $20 \ cm$ is concentric with the capacitor and located halfway between the plates. If the electric field between the plates is changing at the rate of $3.6 \times 10^{12} \ V/(m \cdot s)$,then the displacement current through the loop is (Assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$) (in $A$)

Who first produced electromagnetic waves?