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?

$A$ 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 $C R .$ )

$A$ 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 . . . . . . $\text{V s}^{-1}$.

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

The source of an electromagnetic wave can be a charge

An infinitely long thin wire carrying a uniform linear static charge density $\lambda$ is placed along the $z-$axis. The wire is set into motion along its length with a uniform velocity $\vec{V} = v\hat{k}$. Calculate the Poynting vector $\vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B})$.