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 $Vs^{-1}$)

Write the Ampere-Maxwell law in the form of an equation.

Match List-$I$ with List-$II$.

List-$I$ (Relation)	List-$II$ (Law)
$A$. $\oint \overrightarrow{E} \cdot d\vec{l} = -\frac{d}{dt} \oint \overrightarrow{B} \cdot d\vec{a}$	$I$. Ampere's circuital law
$B$. $\oint \vec{B} \cdot d\vec{l} = \mu_0(I + \epsilon_0 \frac{d\phi_E}{dt})$	$II$. Faraday's laws of electromagnetic induction
$C$. $\oint \overrightarrow{E} \cdot d\vec{a} = \frac{1}{\epsilon_0} \int \rho dv$	$III$. Ampere-Maxwell law
$D$. $\oint \overrightarrow{B} \cdot d\vec{l} = \mu_0 I$	$IV$. Gauss's law of electrostatics

Choose the correct answer from the options given below:

Which of the following Maxwell's equations is valid for time-varying conditions but not valid for static conditions?

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).

The capacitance of a capacitor is $2 \ pF$. If the electric field inside the capacitor changes at a rate of $10^{12} \ V \ s^{-1}$,the displacement current is ..... $A$.