Embibe Experts Solutions for Chapter: Electromagnetic Waves, Exercise 1: Exercise

Non-uniform displacement current. Figure shows a circular region of radius $R=3.00 \mathrm{cm}$ in which a displacement current $i_{\mathrm{d}}$ is directed out of the figure. The magnitude of the displacement current is $i_{\mathrm{d}}=(3.00 \mathrm{A})(r/R),$ where $r$ is the radial distance $(r\le R)$ from the center. What is the magnitude of the magnetic field due to $i_{\mathrm{d}}$ at radial distances
(a) $2.00 \mathrm{cm}$ and
(b) $6.00 \mathrm{cm}$?

A capacitor with square plates of edge length $L$ is being discharged by a current of $0.75 \mathrm{A}$ . Figure is a head-on view of one of the plates from inside the capacitor. A dashed rectangular path is shown. If $L=10 \mathrm{cm}$ , $W=4.0 \mathrm{cm},$ $H=2.0 \mathrm{cm},$ and what is the value of $\oint \overrightarrow{B}·d\overrightarrow{s}$ around the dashed path? 

As a parallel-plate capacitor with circular plates $20 \mathrm{cm}$ in diameter is being charged, the current density of the displacement current in the region between the plates is uniform and has a magnitude of $15 \mathrm{A} {\mathrm{m}}^{-2}.$$\left(a\right)$ Calculate the magnitude $B$ of the magnetic field at a distance $r=50 \mathrm{mm}$ from the axis of symmetry of this region. $\left(b\right)$ Calculate $\frac{dE}{dt}$ in this region. 

At what rate must the potential difference between the plates of a parallel-plate capacitor with a $5.0 \mathrm{\mu F}$ capacitance be changed to produce a displacement current of $0.75 A$?

A silver wire has resistivity $\rho =1.62\times {10}^{-8 }\mathrm{\Omega }·\mathrm{m}$ and a cross-sectional area of $5.00 {\mathrm{mm}}^2$. The current in the wire is uniform and changing at the rate of $2000 \mathrm{A} {\mathrm{s}}^{-1}$ When the current is $54.0 \mathrm{A}$ .

$\left(a\right)$ What is the magnitude of the (uniform) electric field in the wire when the current in the wire is$100 \mathrm{A}$?

$\left(b\right)$ What is the displacement current in the wire at that time?

$\left(c\right)$ What is the ratio of the magnitude of the magnetic field due to the displacement current to that due to the current at a distance $r$ from the wire? 

The induced magnetic field at radial distance $6.0 \mathrm{mm}$ from the central axis of a circular parallel-plate capacitor is $1.2\times {10}^{-7 }\mathrm{T}$. The plates have radius $4.0 \mathrm{mm}$ . At what rate $\frac{dE}{dt}$ is the electric field between the plates changing?

Electromagnetic spectrum is commonly classified as gamma rays, X-rays, UV-rays, visible light, IR-rays, etc. Mention very briefly two special features of any three of these, with respect to their production (source) and properties.

Describe very briefly any four regions of electromagnetic spectrum, mentioning their special properties/features.