Electromagnetic Waves

8.9 Energy of a photon is given as:

E = h $\nu$ = $\frac{hc}{\lambda }$ , where

h = Planck’s constant = 6.6 $\times {10}^{-34}$ Js

c = Speed of light = 3 $\times {10}^8$ m/s

$\lambda$ = wavelength of radiation

Hence, E = $\frac{6.6\mathrm{}\times {10}^{-34}\times 3\mathrm{}\times {10}^8}{\lambda }$ J = $\frac{1.98\times {10}^{-25}}{\lambda }$ J = $\frac{1.98\times {10}^{-25}}{\lambda \times 1.602\times {10}^{-19}}$ eV = $\frac{1.236\times {10}^{-6}}{\lambda }$ eV

The following table lists the photon energies for

8.8 Electric field amplitude, $E_0$ = 120 N/C

Frequency of source, $\nu$ = 50 MHz = 50 $\times {10}^6$ Hz

Speed of light, c = 3 $\times {10}^8$ m/s

Magnitude of magnetic field strength is given as

$B_0=$ $\frac{E_0}{c}$ = $\frac{120}{3\mathrm{}\times {10}^8}$ = 4 $\times {10}^{-7}$ T = 400 $\times {10}^{-9}$ T = 400 nT

$\mathrm{A}\mathrm{n}\mathrm{g}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{}\mathrm{i}\mathrm{s}\mathrm{}\mathrm{g}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{}\mathrm{a}\mathrm{s}\mathrm{}$ $\omega$ = 2 $\pi \nu$ = 2 $\times \pi \times$&n

8.7 The amplitude of magnetic field of the electromagnetic wave in a vacuum,

$B_0$ = 510 nT = 510 $*{10}^{-9}$ T

Speed of the light in vacuum, c = 3 $*{10}^8$ m/s

Amplitude of electric field of the electromagnetic wave is given by the relation,

E = c $B_0$ = 3 $*{10}^8*$ 510 $*{10}^{-9}$ N/C = 153 N

8.6 The frequency of an electromagnetic wave produced by the oscillator is the same as that of a charged particle oscillating about its mean position, i.e. ${10}^9$ Hz.

8.5 The lowest tuning frequency ${\nu }_1$ = 7.5 MHz = 7.5 $\times {10}^6$ Hz

The highest tuning frequency ${\nu }_2$ = 12 MHz = 12 $\times {10}^6$ Hz

Speed of light, c = 3 $\times {10}^8$ m/s

The wavelength for lowest tuning frequency, ${\lambda }_1$ = $\frac{c}{{\nu }_1}$ = $\frac{3\mathrm{}\times {10}^8}{7.5\mathrm{}\times {10}^6}$ = 40 m

The wavelength for highest tuning freq

8.4 The electromagnetic wave travels in a vacuum along the z- direction. The electric field (E) and the magnetic field (H) are in the x-y plane. They are mutually perpendicular.

Frequency of the wave, $\nu$ = 30 MHz = 30 $\times {10}^6$ /s

Speed of light in vacuum, c = 3 $\times {10}^8$ m/s

Wavelength

8.3 The speed of light (3 $*{10}^8$ m/s) in a vacuum is the same for all wavelengths. It is independent of the wavelength in the vacuum.

8.2 Radius of each circular plate, R = 6.0 cm = 0.06 m

Capacitance of parallel capacitor, C = 100 pF = 100 $\times {10}^{-12}$ F

Supply voltage, V = 230 V

Angular frequency, $\omega$ = 300 rad/s

rms value of the conduction current, I = $\frac{V}{X_c}$ , where $X_c=\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}=\mathrm{}\frac{1}{\mathrm{\omega }\mathrm{C}}$

Hence, I = V $\times \omega \times C$ = 230 $\times 300\times$ 100 $\times {10}^{-12}$ = 6

8.1 Radius of the each circular plate, r = 12 cm = 0.12

Distance between the plates, d = 5 cm = 0.05 m

Charging current, I = 0.15 A

Permittivity of free space, ${?}_0$ = 8.85 $\times {10}^{-12}$ $C^2{N}^{-1}{m}^{-2}$

Capacitance between two plates is given by the relation,

C = $\frac{{?}_{0}A}{d}$  , where A = Area of each plate = $?r^2$ = $?\times {0.12}^2$

C = $\frac{8.85\mathrm{}\times {10}^{-12}\times \mathrm{}?\times {0.12}^2}{0.05}$  = 8.007 $\times {10}^{-12}$

F

Charge

Electromagnetic waves do not require a medium to propagate because they generate self-sustaining oscillations of magnetic and electric fields. Hence, it can travel through the vacuum of space. A changing magnetic field generates an electric field and vice versa. This property allows the wave to carr