JEE Physics Electromagnetic Waves MCQs Set 05

Practice MCQs for JEE Physics Electromagnetic Waves

Access targeted multiple-choice questions for Electromagnetic Waves designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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Multiple Choice Questions

Question 1: The energy of em waves is of the order of 15 keV. To which part of the spectrum do they belong?
(a) Ultraviolet
(b) Gamma rays
(c) X-rays
(d) Infra-red rays
Show Answer & Explanation

Answer: (c) X-rays

Explanation:
1. \( \lambda=\frac{1240\ \text{eV nm}}{15000\ \text{eV}}\approx0.08\ \text{nm} \) = 0.8 angstrom, which is in the X-ray range.

Teacher's Note:
1. Wavelengths near 1 angstrom are X-rays.

Question 2: Light with an energy flux of \( 25\times10^4\ \text{W m}^{-2} \) falls on a perfectly reflecting surface at normal incidence. If the surface area is \( 15\ \text{cm}^2 \), the average force exerted on the surface is:
(a) \( 1.25\times10^{-6} \) N
(b) \( 2.50\times10^{-6} \) N
(c) \( 1.20\times10^{-6} \) N
(d) \( 3.0\times10^{-6} \) N
Show Answer & Explanation

Answer: (b) \( 2.50\times10^{-6} \) N

Explanation:
1. \( F=\frac{2IA}{c}=\frac{2\times25\times10^4\times15\times10^{-4}}{3\times10^8}=2.5\times10^{-6}\ \text{N} \)

Teacher's Note:
1. Radiation force on a perfect reflector is 2IA/c.

Question 3: The condition under which a microwave oven heats up a food item containing water molecules most efficiently is:
(a) Microwaves are heat waves, so always produce heating
(b) Infra-red waves produce heating in a microwave oven
(c) The frequency of the microwaves must match the resonant frequency of the water molecules
(d) The frequency of the microwaves has no relation with the natural frequency of water molecules
Show Answer & Explanation

Answer: (c) The frequency of the microwaves must match the resonant frequency of the water molecules

Explanation:
1. Maximum energy is absorbed when the driving frequency matches a natural (rotational) frequency of the water molecule.

Teacher's Note:
1. Resonant absorption heats the food most efficiently.

Question 4: An electromagnetic wave of frequency 3.0 MHz passes from vacuum into a dielectric medium with relative permittivity 4.0. Then:
(a) Wavelength is doubled and frequency becomes half
(b) Wavelength is halved and frequency remains unchanged
(c) Wavelength and frequency both remain unchanged
(d) Wavelength is doubled and frequency unchanged
Show Answer & Explanation

Answer: (b) Wavelength is halved and frequency remains unchanged

Explanation:
1. \( n=\sqrt{\epsilon_r}=2 \); frequency stays the same and \( \lambda'=\lambda/2 \).

Teacher's Note:
1. Frequency is fixed by the source; speed and wavelength shrink by the refractive index.

Question 5: The ratio of the amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to:
(a) The speed of light in vacuum
(b) Reciprocal of the speed of light in vacuum
(c) The ratio of magnetic permeability to the electric susceptibility of vacuum
(d) Unity
Show Answer & Explanation

Answer: (b) Reciprocal of the speed of light in vacuum

Explanation:
1. \( \frac{B_0}{E_0}=\frac1c \)

Teacher's Note:
1. E0 equals c times B0.

Question 6: The electric and magnetic fields associated with an em wave propagating along the +x axis can be represented by:
(a) \( \vec E=E_0\hat i,\ \vec B=B_0\hat j \)
(b) \( \vec E=E_0\hat k,\ \vec B=B_0\hat i \)
(c) \( \vec E=E_0\hat j,\ \vec B=B_0\hat i \)
(d) \( \vec E=E_0\hat j,\ \vec B=B_0\hat k \)
Show Answer & Explanation

Answer: (d) \( \vec E=E_0\hat j,\ \vec B=B_0\hat k \)

Explanation:
1. The direction of propagation is along \( \vec E\times\vec B \). Only \( \hat j\times\hat k=\hat i \) gives +x.

Teacher's Note:
1. E, B and the propagation direction form a right-handed triad.

Question 7: The decreasing order of wavelength of infrared, microwave, ultraviolet and gamma rays is:
(a) Microwave, infrared, ultraviolet, gamma rays
(b) Gamma rays, ultraviolet, infrared, microwaves
(c) Microwaves, gamma rays, infrared, ultraviolet
(d) Infrared, microwave, ultraviolet, gamma rays
Show Answer & Explanation

Answer: (a) Microwave, infrared, ultraviolet, gamma rays

Explanation:
1. Wavelength decreases through the spectrum: microwave, infrared, ultraviolet, gamma.

Teacher's Note:
1. Gamma rays have the smallest wavelength and microwaves the largest here.

Question 8: The electric field of an electromagnetic wave in free space is given by \( \vec E=10\cos(10^7t+kx)\hat j \) V/m, where t and x are in seconds and metres. Consider: (1) The wavelength 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 the +x direction. Which pair of statements is correct?
(a) (3) and (4)
(b) (1) and (2)
(c) (2) and (3)
(d) (1) and (3)
Show Answer & Explanation

Answer: (d) (1) and (3)

Explanation:
1. \( k=\frac\omega c=\frac{10^7}{3\times10^8}=0.033\ \text{rad/m} \), so (2) is false.
2. \( \lambda=\frac{2\pi}{k}=188.4\ \text{m} \) so (1) is true; amplitude is 10 V/m (3) true; the phase \( kx+\omega t \) means propagation along -x, so (4) is false.

Teacher's Note:
1. The sign between kx and omega t gives the direction of travel.

Question 9: The electric field part of an electromagnetic wave in a medium is represented by \( E_x=0,\ E_y=2.5\cos\left[(2\pi\times10^6)t-(\pi\times10^{-2})x\right]\ \text{N/C},\ E_z=0 \). The wave is:
(a) Moving along x direction with frequency \( 10^6 \) Hz and wavelength 100 m
(b) Moving along x direction with frequency \( 10^6 \) Hz and wavelength 200 m
(c) Moving along -x direction with frequency \( 10^6 \) Hz and wavelength 200 m
(d) Moving along y direction with frequency \( 2\pi\times10^6 \) Hz and wavelength 200 m
Show Answer & Explanation

Answer: (b) Moving along x direction with frequency \( 10^6 \) Hz and wavelength 200 m

Explanation:
1. Phase \( \omega t-kx \) means travel along +x. \( f=\frac{2\pi\times10^6}{2\pi}=10^6\ \text{Hz} \); \( \lambda=\frac{2\pi}{\pi\times10^{-2}}=200\ \text{m} \).

Teacher's Note:
1. Read the frequency from omega and the wavelength from k.

Question 10: The velocity of electromagnetic radiation in a medium of permittivity \( \epsilon_0 \) and permeability \( \mu_0 \) is given by:
(a) \( \frac1{\sqrt{\mu_0\epsilon_0}} \)
(b) \( \sqrt{\frac{\mu_0}{\epsilon_0}} \)
(c) \( \sqrt{\frac{\epsilon_0}{\mu_0}} \)
(d) \( \sqrt{\mu_0\epsilon_0} \)
Show Answer & Explanation

Answer: (a) \( \frac1{\sqrt{\mu_0\epsilon_0}} \)

Explanation:
1. Maxwell's equations give \( c=\frac1{\sqrt{\mu_0\epsilon_0}} \).

Teacher's Note:
1. The speed of light follows from the two constants of free space.

Question 11: If \( \lambda_v,\lambda_x \) and \( \lambda_m \) represent the wavelengths of visible light, X-rays and microwaves respectively, then:
(a) \( \lambda_m>\lambda_x>\lambda_v \)
(b) \( \lambda_m>\lambda_v>\lambda_x \)
(c) \( \lambda_v>\lambda_x>\lambda_m \)
(d) \( \lambda_v>\lambda_m>\lambda_x \)
Show Answer & Explanation

Answer: (b) \( \lambda_m>\lambda_v>\lambda_x \)

Explanation:
1. Microwaves have centimetre wavelengths, visible light about 500 nm, X-rays about 0.1 nm.

Teacher's Note:
1. Order the spectrum by wavelength.

Question 12: We consider the radiation emitted by the human body. Which one of the following statements is true?
(a) The radiation emitted is in the infra-red region
(b) The radiation is emitted only during the day
(c) The radiation is emitted during the summers and absorbed during the winters
(d) The radiation emitted lies in the ultraviolet region and hence is not visible
Show Answer & Explanation

Answer: (a) The radiation emitted is in the infra-red region

Explanation:
1. A body at about 310 K has its peak emission near 9 micrometre, in the infrared.

Teacher's Note:
1. Wien's law puts body-temperature radiation in the infrared.

Question 13: Which of the following rays are not electromagnetic waves?
(a) X-rays
(b) Gamma rays
(c) Beta rays
(d) Heat rays
Show Answer & Explanation

Answer: (c) Beta rays

Explanation:
1. Beta rays are streams of electrons, which are particles.

Teacher's Note:
1. Only the beta rays consist of material particles.

Question 14: What is the cause of the green house effect?
(a) Infra-red rays
(b) Ultra violet rays
(c) X-rays
(d) Radio waves
Show Answer & Explanation

Answer: (a) Infra-red rays

Explanation:
1. Greenhouse gases absorb and re-radiate infrared radiation emitted by the Earth, trapping heat.

Teacher's Note:
1. The Earth's heat radiation lies in the infrared.

Question 15: The biological importance of the ozone layer is:
(a) It stops ultraviolet rays
(b) Ozone layer reduces the green house effect
(c) Ozone layer reflects radio waves
(d) Ozone layer controls the O2/H2 ratio in the atmosphere
Show Answer & Explanation

Answer: (a) It stops ultraviolet rays

Explanation:
1. Ozone absorbs harmful ultraviolet radiation from the Sun.

Teacher's Note:
1. Ozone shields living things from UV.

Question 16: The frequency order for gamma rays (B), X-rays (A) and UV rays (C) is:
(a) \( B>A>C \)
(b) \( A>B>C \)
(c) \( C>B>A \)
(d) \( A>C>B \)
Show Answer & Explanation

Answer: (a) \( B>A>C \)

Explanation:
1. Frequency decreases from gamma rays to X-rays to ultraviolet.

Teacher's Note:
1. Gamma rays have the highest frequency of the three.

Question 17: The wavelength of light of frequency 100 Hz is:
(a) \( 4\times10^6 \) m
(b) \( 3\times10^6 \) m
(c) \( 2\times10^6 \) m
(d) \( 5\times10^{-5} \) m
Show Answer & Explanation

Answer: (b) \( 3\times10^6 \) m

Explanation:
1. \( \lambda=\frac cf=\frac{3\times10^8}{100}=3\times10^6\ \text{m} \)

Teacher's Note:
1. Wavelength equals c over frequency.

Question 18: If \( \epsilon_0 \) and \( \mu_0 \) are the electric permittivity and magnetic permeability of free space, and \( \epsilon \) and \( \mu \) are the corresponding quantities in a medium, the refractive index of the medium is:
(a) \( \sqrt{\frac{\epsilon_0\mu_0}{\epsilon\mu}} \)
(b) \( \sqrt{\frac{\epsilon\mu}{\epsilon_0\mu_0}} \)
(c) \( \sqrt{\frac{\epsilon_0\mu}{\epsilon\mu_0}} \)
(d) \( \sqrt{\frac\epsilon{\epsilon_0}} \)
Show Answer & Explanation

Answer: (b) \( \sqrt{\frac{\epsilon\mu}{\epsilon_0\mu_0}} \)

Explanation:
1. \( n=\frac cv=\frac{1/\sqrt{\mu_0\epsilon_0}}{1/\sqrt{\mu\epsilon}}=\sqrt{\frac{\epsilon\mu}{\epsilon_0\mu_0}} \)

Teacher's Note:
1. Refractive index is the ratio of the speeds of light.

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