Inside a parallel plate capacitor,the electric field $E$ varies with time as $t^2$. The variation of the induced magnetic field with time is given by

Write Maxwell's equations.

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).

The source of a time-varying magnetic field may be:
$(A)$ A permanent magnet
$(B)$ An electric field changing linearly with time
$(C)$ Direct current
$(D)$ A decelerating charged particle
$(E)$ An antenna fed with a digital signal
Choose the correct answer from the options given below:

The charge on a capacitor varies with time as $q = q_0 \sin(2\pi nt)$. What is the displacement current produced in the dielectric of the capacitor?

Which equations are called Maxwell's equations?