Displacement Current, Maxwell's Equations & Production

Match List - I with List - II.

Choose the correct answer from the options given below:

A displacement current of 4.0 A can be set up in the space between two parallel plates of $6\ \mu\text{F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^{6}\text{ V/s}$. The value of $\alpha$ is ______.

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma = 10\text{ mho/m}$. The ratio of maximum conduction current density to maximum displacement current density is ______.

$[$ Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2 ]$

If $\epsilon_0$ 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 dimensions of $\left(\epsilon_0 \frac{d\phi_E}{dt}\right)$ are that of:

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 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _________ $\text{Vs}^{-1}$.

A parallel plate capacitor of area $A = 16\text{ cm}^{2}$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $\text{A}_0 = 3.2\text{ cm}^{2}$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $\text{A}_0$ is __________ mA.

An alternating voltage of amplitude $40\text{ V}$ and frequency $4\text{ kHz}$ is applied directly across the capacitor of $12\ \mu\text{F}$. The maximum displacement current between the plates of the capacitor is nearly:

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions:

Match List I with List II

Choose the correct answer from the options given below:

The rms value of conduction current in a parallel plate capacitor is $6.9\ \mu\text{A}$. The capacity of this capacitor, if it is connected to $230\text{ V}$ ac supply with an angular frequency of $600\text{ rad/s}$, will be:

The displacement current of 4.425 $\mu$A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106 Vs${}^{-1}$. The area of each plate of the capacitor is 40 cm2. The distance between each plate of the capacitor is x $\times$ 10$-$3 m. The value of x is __________.

(Permittivity of free space, $\varepsilon_0$ = 8.85 $\times$ 10$-$12 C2 N${}^{-1}$ m${}^{-2}$).

Seawater at a frequency f = 9 $\times$ 102 Hz, has permittivity $\varepsilon$ = 80$\varepsilon$0 and resistivity $\rho$ = 0.25 $\Omega$m. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V(t) = V0 sin(2$\pi$ft). Then the conduction current density becomes 10x times the displacement current density after time t = $\frac{1}{800}$ s. The value of x is _____________. (Given: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$ Nm2C${}^{-2}$)

Out of the following options which one can be used to produce a propagating electromagnetic wave?

A parallel plate capacitor of area 60 cm$^{2}$ and separation 3 mm is charged initially to 90$\mu$C. If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of $2.5 \times 10^{-8}$ C/s, then what is the magnetic field between the plates?

The electromagnetic radiations are caused by