$A$ variable frequency $AC$ source is connected to a capacitor. How will the displacement current change with a decrease in frequency?

Which scientist first time produced electromagnetic waves in laboratory?

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:

If $\varepsilon_0$ denotes the permittivity of free space and $\phi_{E}$ is the flux of the electric field through the area bounded by the closed surface,then the dimensions of $\left(\varepsilon_0 \frac{d \phi_{E}}{dt}\right)$ are that of

Write the $SI$ unit of ${\epsilon _0}\left( {\frac{{d{\Phi _E}}}{{dt}}} \right)$.

$A$ parallel plate capacitor with circular plates of radius $1\, m$ has a capacitance of $1 \;nF$. At $t=0,$ it is connected for charging in series with a resistor $R=1 \;M \Omega$ across a $2 \;V$ battery (Figure). Calculate the magnetic field at a point $P$,halfway between the centre and the periphery of the plates,after $t=10^{-3}\; s$.
(The charge on the capacitor at time $t$ is $q(t)=C V[1-\exp (-t / \tau)],$ where the time constant $\tau$ is equal to $C R .$ )