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

$A$ 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 $C R .$ )

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

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

$A$ cylindrical region contains a uniform electric field that is along the cylinder axis and is changing with time. If $r$ is the distance from the cylinder axis,the magnitude of the magnetic field within the region is:

Which scientist first time produced electromagnetic waves in laboratory?