$A$ 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.

Imagine a world where free magnetic charges exist. In this world,a circuit is made with a $U$-shape wire and a rod free to slide on it. $A$ current carried by free magnetic charges can flow in the circuit. When the circuit is placed in a uniform electric field $E$ perpendicular to the plane of the circuit and the rod is pulled to the right with a constant speed $v$,the magnetic $emf$ in the circuit and the direction of the corresponding current,arising because of changing electric flux will be ($l$ is the length of the rod and $c$ is the speed of light).

An electromagnetic wave of frequency $100 \text{ MHz}$ propagates through a medium of conductivity $\sigma = 10 \text{ mho/m}$. The ratio of maximum conducting current density to maximum displacement current density is . . . . . . . $\left[ \text{Take } \frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \right]$

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

$A$ long straight cable of length $l$ is placed symmetrically along $z-$ axis and has radius $a (a << l)$. The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I(t) = I_0 \sin(2\pi \nu t)$ flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance $s$ from the wire inside the cable is $\vec{E}(s,t) = \mu_0 I_0 \nu \cos(2\pi \nu t) \ln(s/a) \hat{k}$.
$(i)$ Calculate the displacement current density inside the cable.
$(ii)$ Integrate the displacement current density across the cross-section of the cable to find the total displacement current $I_d$.
$(iii)$ Compare the conduction current $I_0$ with the displacement current $I_d$.

An alternating voltage of amplitude $40 \, V$ and frequency $4 \, kHz$ is applied directly across a capacitor of $12 \, \mu F$. The maximum displacement current between the plates of the capacitor is nearly: (in $ \, A$)