The displacement current of $4.425 \,\mu A$ is developed in the space between the plates of a parallel plate capacitor when the voltage is changing at a rate of $10^{6} \,V s^{-1}$. The area of each plate of the capacitor is $40 \,cm^{2}$. The distance between the plates of the capacitor is $x \times 10^{-3} \,m$. The value of $x$ is ................ (Permittivity of free space,$\varepsilon_{0} = 8.85 \times 10^{-12} \,C^{2} N^{-1} m^{-2}$)

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

Which is the missing term in Ampere's circuital law?

According to Maxwell's hypothesis,a changing electric field gives rise to

$A$ 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 $A$)

$A$ parallel plate capacitor with plate area $A$ and separation between the plates $d$ is charged by a constant current $i$. Consider a plane surface of area $A/2$ parallel to the plates and drawn symmetrically between the plates. The displacement current through this area will be: