Question 21:
easyThe ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to:
(2012 Mains)
The speed of an electromagnetic wave in vacuum is related to the field amplitudes by $c = \frac{E_0}{B_0}$ . Rearranging this, we get the ratio of magnetic to electric field amplitude as $\frac{B_0}{E_0} = \frac{1}{c}$ . Therefore, it is the reciprocal of the speed of light in vacuum.
Question 22:
easyThe dimensions of $(\mu_0\epsilon_0)^{-\frac{1}{2}}$ are:
(2011 Pre)
The expression $(\mu_0\epsilon_0)^{-\frac{1}{2}} = \frac{1}{\sqrt{\mu_0\epsilon_0}}$ represents the speed of light in vacuum (c). The dimensional formula for velocity or speed is $[L T^{-1}]$ .
Question 23:
easyThe electric and the magnetic field associated with an e.m. wave, propagating along the +z axis, can be represented by:
(2011 Pre)
The direction of propagation of an electromagnetic wave is parallel to the Poynting vector, given by the cross product $\bar{E} \times \bar{B}$ . For option a, $\hat{i} \times \hat{j} = \hat{k}$ , which corresponds to the +z axis.
Question 24:
easyThe electric field of an electromagnetic wave in free space is given by $E = 10\cos(10^7 t + kx)\hat{j} V/m$ where t and x are in second and metres respectively. It can be inferred that
1. The wavelength $\lambda$ is $188.4 m$
2. The wave number k is $0.33 rad/m$
3. The wave amplitude is $10 V/m$
4. The wave is propagating along +x direction
Where one of the following pairs of statement is correct?
(2010 Mains)
Comparing with standard form $E = E_0\cos(\omega t + kx)$ , amplitude $E_0 = 10 V/m$ (Statement 3 is correct). Angular frequency $\omega = 10^7 rad/s$ , so wave number $k = \frac{\omega}{c} = \frac{10^7}{3 \times 10^8} = 0.033 rad/m$ . Wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{0.033} \approx 188.4 m$ (Statement 1 is correct). The positive sign indicates propagation in the -x direction. Thus, 1 and 3 are correct.
Question 25:
easyWhich of the following statement is false for the properties of electromagnetic waves?
(2010 Pre)
In an electromagnetic wave, the oscillating electric and magnetic field vectors are mutually perpendicular to each other, not parallel. They are also perpendicular to the direction of propagation. Thus, option d is false.
Question 26:
easyThe frequency order for $\gamma$ -rays (b), X-rays (a), UV-rays (c) is
(2000)
Frequency is inversely proportional to wavelength. The order of increasing wavelength is $\gamma$ -rays, X-rays, UV-rays. Thus, the order of decreasing frequency is $\gamma$ -rays > X-rays > UV-rays, which corresponds to $b > a > c$ .
Question 27:
easyWhich of the following electromagnetic radiations have the smaller wavelength?
(1994)
Among the given electromagnetic radiations, $\gamma$ -rays have the highest frequency and therefore the smallest wavelength, following the relation $c = \nu \lambda$ .
Question 28:
easyThe structure of solids is investigated by using
(1992)
X-rays have wavelengths on the order of atomic spacings in solids. They are diffracted by the crystal lattice, making them suitable for investigating the structure of solids (X-ray crystallography).
Question 29:
easyWhich of the following electromagnetic radiations have the longest wavelength?
(1989)
In the electromagnetic spectrum, radio waves possess the lowest frequency and therefore the longest wavelength among all the given options.
Question 30:
easyWhen light propagates through a material medium of relative permittivity $\epsilon_r$ and relative permeability $\mu_r$ , the velocity of light, v is given by : (c – velocity of light in vacuum)
(2022)
The velocity of light in a medium is given by $v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{1}{\sqrt{\mu_0 \mu_r \epsilon_0 \epsilon_r}}$ . Since the speed of light in vacuum is $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ , we get $v = \frac{c}{\sqrt{\epsilon_r \mu_r}}$ .