In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0×10¹⁰ Hz and amplitude 48 V/m.
i) What is the wavelength of the wave?
ii) What is the amplitude of the oscillating magnetic field?
iii) Show that, the average energy density of the E field equals the average energy density of the B field. (Take, $\left.\mathrm{c}=3\times {10}^8\frac{\mathrm{m}}{\mathrm{s}}\right)$

OR

(i) Which segment of electromagnetic waves has the highest frequency? How are these waves produced? Give one use of these waves.

(ii) Which EM waves lie near the high frequency end of the visible part of the EM spectrum? Give its one use. In what way, this component of light has harmful effects on humans?
 

Frequency of the electromagnetic wave, ν = 2.0 × 1010 Hz
Electric field amplitude, E0 = 48 V m−1
Speed of light, c = 3 × 108 m/s
1. Wavelength of a wave is given as:
$\begin{array}{l}\mathrm{\lambda }=\frac{\mathrm{c}}{\mathrm{v}}\\ =\frac{3\times {10}^8}{2\times {10}^{10}}=0.015\mathrm{m}\end{array}$
2. Magnetic field strength is given as:
$\begin{array}{l}{\mathrm{B}}_0=\frac{{\mathrm{E}}_0}{\mathrm{c}}\\ =\frac{48}{3\times {10}^8}=1.6\times {10}^{-7}\mathrm{T}\end{array}$
3. Energy density of the electric field is:
${\mathrm{U}}_{\mathrm{E}}=\frac{1}{2}{\mathrm{ϵ}}_0{\mathrm{E}}^2$
And, energy density of the magnetic field is: ${\mathrm{U}}_{\mathrm{B}}=\frac{1}{2{\mathrm{\mu }}_0}{\mathrm{B}}^2$
Where,
∈₀ = Permittivity of free space
μ₀ = Permeability of free space
We have the relation connecting E and B as:
$\mathrm{c}=\frac{1}{\sqrt{{\mathrm{ϵ}}_0{\mathrm{\mu }}_0}}$
E = cB … (1)
Where,
$\mathrm{E}=\frac{1}{\sqrt{{\mathrm{ϵ}}_0{\mathrm{\mu }}_0}}\mathrm{B}$
$$\begin{gathered} \text{ Energy density due to the electric field, }{\mathrm{U}}_{\mathrm{E}}=\frac{1}{2}{ϵ}_0{\mathrm{E}}^2 \\ \text{ Energy density due to the magnetic field, }{\mathrm{U}}_{\mathrm{B}}=\frac{1}{2}{\mathrm{B}}^2/{\mathrm{\mu }}_{\mathrm{o}} \\ \text{ also, }\mathrm{c}=\frac{1}{\sqrt{{\mathrm{ϵ}}_0{\mathrm{\mu }}_0}} \\ \text{ on solving above equations, }{\mathrm{U}}_{\mathrm{E}}={\mathrm{U}}_{\mathrm{B}} \end{gathered}$$

OR

I. Gamma rays have the highest energies, the shortest wavelengths, and the highest frequencies.
Electromagnetic waves are produced whenever electric charges are accelerated. This makes it possible to produce electromagnetic waves by letting an alternating current flow through a wire, an antenna. The frequency of the waves created in this way equals the frequency of the alternating current.

II. Ultraviolet rays lie near the high frequency end of visible part of EM spectrum. They are used to sterilize drinking water and surgical instruments.
General eye irritation and cataracts have sometimes been reported in workers exposed to high levels of radiofrequency and microwave radiation, but animal studies do not support the idea that such forms of eye damage can be produced at levels that are not thermally hazardous.