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 $t = ..... \ \mu s$.

$A$ parallel plate capacitor of area $A = 16 \ cm^2$ and separation between the plates $10 \ cm$ is charged by a $DC$ current. Consider a hypothetical plane surface of area $A_0 = 3.2 \ cm^2$ inside the capacitor and parallel to the plates. At an instant,the current through the circuit is $6 \ A$. At the same instant,the displacement current through $A_0$ is . . . . . . $mA$.

In the charging of a capacitor,what is the contradiction in Ampere's circuital law?

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

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

Who produced electromagnetic waves for the first time?