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

$A$ parallel plate capacitor is charged by connecting it to a battery through a resistor. If $I$ is the current in the circuit,then in the gap between the plates:

$A$ time-varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5 \mu \text{F}$. The dielectric constant of the medium between the capacitor plates is $1$. It produces an instantaneous displacement current of $0.25 \text{ mA}$ in the intervening space between the capacitor plates. The magnitude of the rate of change of the potential difference will be . . . . . . $\text{V s}^{-1}$.

$A$ parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is

$A$ plane electromagnetic wave of angular frequency $\omega$ propagates in a poorly conducting medium of conductivity $\sigma$ and relative permittivity $\varepsilon$. Find the ratio of conduction current density and displacement current density in the medium.

Sea water at frequency $v = 4 \times 10^8\, Hz$ has permittivity $\epsilon \approx 80\epsilon_0$,permeability $\mu = \mu_0$ and resistivity $\rho = 0.25\,\Omega m$. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source $V(t) = V_0 \sin(2\pi vt)$. What fraction of the conduction current density is the displacement current density?