WBCHSE Class 12 Physics Electromagnetic Waves Question And Answers

Physics Electromagnetic Waves Questions And Answers

Question 1. Sound waves, unlike electromagnetic waves, cannot travel through a vacuum. Why?

Answer:

Sound is produced by the mechanical vibration of a body. Mechanical vibrations need a material medium with inertia and elasticity to sustain it for propagation. Hence, sound waves cannot travel through a vacuum.

On the other hand, electromagnetic waves are set up due to the oscillation of electric and magnetic fields. Electric and magnetic fields can spread without any medium. Hence, electromagnetic waves can travel through a vacuum.

Question 2. Electric fields or magnetic fields can independently exist in nature, but in electromagnetic waves, neither electric fields nor magnetic fields can exist independently. Why?

Answer:

The electric field or magnetic field, which does not vary with time, can exist independently. But fields, varying with time, cannot exist independently. Because during progression, the two fields continually create each other.

As varying electric and magnetic fields generate electromagnetic waves, none of the two fields of an electromagnetic wave can exist independently.

Question 3. The electric field and magnetic field of an electromagnetic wave advance as sinusoidal waves. Instead of being sinusoidal, If these fields had been different periodical waves, state whether any electromagnetic wave would have been formed or not.

Answer:

Any periodic wave can be expressed as a mixture of a large number of sinusoidal waves. The frequency of these waves is an integral multiple of the frequency of the main wave.

Hence, in this case, electromagnetic waves will be formed. It will contain many electromagnetic waves of different frequencies.

WBBSE Class 12 Electromagnetic Waves Q&A

Question 4. Name any two electromagnetic waves. State any one similarity and one dissimilarity between them.

Answer:

1. Radio wave,
2. Gamma rays.

Similarity: Each is a transverse wave traveling with the velocity of light.

Dissimilarity: Radio waves are used as carrier waves in distant communication, but gamma rays cannot be. On the other hand, gamma rays can initiate nuclear reactions, whereas radio waves can not.

Question 5. Light waves can travel in a vacuum but sound waves require a material medium. Why?

Answer:

A sound wave is an elastic wave. It travels by using the property of elasticity of material media. On the other hand, a light wave is an electromagnetic wave—the propagation of electric and magnetic fields does not need any Medium.

Short Answer Questions on Electromagnetic Spectrum

Class 12 Physics Electromagnetic Waves Short Questions And Answers

Question 1. A capacitor is made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source. The charging current is constant and equal to 0.15 A.

1. Calculate the capacitance and rate of change of potential difference between the plates.
2. Obtain the displacement current across the plates.
3. Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

Answer:

1. ∵ \(V=\frac{Q}{C} \quad \text { or, } \frac{d V}{d t}=\frac{1}{C} \frac{d Q}{d t}=\frac{I}{C}\)

In this case,

⇒ \(C=\frac{\epsilon_0 A}{d}=\frac{8.854 \times 10^{-12} \times 3.14 \times\left(12 \times 10^{-2}\right)^2}{5 \times 10^{-2}}\)

= 8 x 10^-12 F = 8 pF

∴ \(\frac{d V}{d t}=\frac{I}{C}=\frac{0.15}{8 \times 10^{-12}}=1.875 \times 10^{10} \mathrm{~V} \cdot \mathrm{s}^{-1}\)

2. Displacement current,

⇒ \(I_d=\epsilon_0 \frac{d \phi_E}{d t}=\epsilon_0 \frac{d}{d t}(E A)=\epsilon_0 A \frac{d E}{d t}=\frac{\epsilon_0 A}{d} \cdot \frac{d V}{d t}\)

⇒ \(C \cdot \frac{d V}{d t}=8 \times 10^{-12} \times 1.875 \times 10^{10}=0.15 \mathrm{~A}\)

3. Yes, because the conduction current entering a plate and the displacement current of the plate are identical.

Question 2. Which physical quantity is the same for X-rays of wavelength 10^-10 m, red light of wavelength 6800 Å, and radio waves of wavelength 500 m?

Answer:

The speed of electromagnetic waves in a vacuum is fixed and is equal to 3 x l0⁸ m. s^-1. Since all three waves (viz. X-ray, redlight, and radio waves) are electromagnetic, their speed in vacuum remains the same.

Practice Questions on Applications of Electromagnetic Waves

Question 3. A plane electromagnetic wave travels in a vacuum along the z direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?

Answer:

In this case, the electric field \(\bar{E}\) and magnetic field \(\bar{B}\) perpendicular to to other and lie on the xy -plane.

∵ c = fλ

∴ \(\lambda=\frac{c}{f}=\frac{3 \times 10^8}{30 \times 10^6}=10 \mathrm{~m}\)

Question 4. A charged particle oscillates about its mean equilibrium position with a frequency of 10⁹ Hz. What is the frequency of the electromagnetic waves produced by the oscillator?

Answer:

The frequency of the oscillator and the frequency of the electromagnetic wave produced by it are the same. So in this case the frequency of the electromagnetic wave is 10⁹ Hz.

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Question 5. In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 x 10¹⁰ Hz and an amplitude of 48 V. m^-1.

1. What is the wavelength of the wave?
2. What is the amplitude of the oscillating magnetic field?

Answer:

1. ∵ c = fλ

∴ \(\lambda=\frac{c}{f}=\frac{3 \times 10^8}{2.0 \times 10^{10}}=1.5 \times 10^{-2} \mathrm{~m}\)

2. ∵ \(c=\frac{E_0}{B_0}\)

∴ \(B_0=\frac{E_0}{c}=\frac{48}{3 \times 10^8}=1.6 \times 10^{-7} \mathrm{~T}\)

Question 6. Suppose that the electric field part of an electromagnetic wave in a vacuum is

\(\vec{E}\) = [(3.1 N.C^-1)cos{(1.8 rad.m^-1)y + (5.4 x 10⁶ rad. s^-1)t}]\(\hat{i}\)

1. What is the direction of propagation?
2. What is the wavelength, λ?
3. What is the frequency, f?
4. What is the amplitude of the magnetic field part of the wave?
5. Write an expression for the magnetic field part of the wave.

Answer:

The given equation

⇒ \(\vec{E}\) = [3.1 cos(1.8y + 5.4 x 10⁶t)]\(\hat{i}\) → (1)

may be compared with the standard equation of the electric field

⇒ \(\vec{E}\) = [E₀ cos(ky + ωt)]\(\hat{i}\) →(2)

and following conclusions drawn.

1. Along \(\hat{-j}\) direction (∵ coefficient of y is positive).
2. Wavelength, \(\lambda=\frac{2 \pi}{k}=\frac{2 \times 3.14}{1.8}=3.49 \mathrm{~m}\)
3. Frequency, \(f=\frac{\omega}{2 \pi}=\frac{5.4 \times 10^6}{2 \times 3.14}=0.86 \mathrm{MHz}\)
4. \(B_0=\frac{E_0}{c}=\frac{3.1}{3 \times 10^8}=10 \mathrm{nT}\)
5. \(\vec{B}\) = [B₀ cos(ky + (ωt)]\(\hat{k}\)

= [10 cos(1.8y + 5.4 x 10⁶ t)] \(\hat{k}\) nT

Question 7. Given below are some famous numbers associated with electromagnetic radiations in different contexts in physics. State the part of the electromagnetic spectrum to which each belongs.

1. 21 cm (wavelength emitted by atomic hydrogen in interstellar space)
2. 1057 MHz (frequency of radiation arising from two close energy hydrogen, known as Lamb shift)
3. 5890 Å-5896 Å (double lines of sodium)
4. 14.4 keV [energy of a particular transition in ⁵⁷Fe nucleus associated with a famous high-resolution spectroscopic method (Mossbouer spectroscopy)]

Answer:

1. λ = 21 cm, is of the order of 10^-2 m. i.e., the wavelength lies in the short radio wave region.
2. f = 1057 MHz = 1.057 x 10⁹ Hz, which is in the short radio wave region.
3. λ = 5890 Å – 5896 Å i.e.„ the wavelengths fall in the visible radiation (these are yellow lights of sodium).
4. \(\lambda=\frac{h c}{E e}=\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{14.4 \times 10^3 \times 1.6 \times 10^{-19}}=8.6 \times 10^{-11} \mathrm{~m}\)
5. This wavelength is in the X-ray or soft gamma-ray region.

Question 8. Why do long-distance radio broadcasts use short-wave bands?

Answer:

Only radio waves of short wavelengths can be reflected from the ionosphere of Earth’s atmosphere. Long-distance radio broadcasts use these sky waves.

Question 9. Why use of satellites is necessary for long-distance TV transmission?

Waves of very high frequency necessary for long-distance TV transmission get transmitted through the ionosphere. The satellite is used to return these signals to Earth.

Question 10. Optical and radio telescopes are built on the ground but X-ray astronomy is possible only from satellites orbiting the earth. Why?

Answer:

The earth can receive visible and radio waves coming from the extra-terrestrial objects as the atmosphere can transmit these rays.

But the atmosphere absorbs X-rays and hence an X -telescope cannot receive these signals when set up on the ground. Thus an X-ray telescope has to be set up in a satellite orbiting the earth.

Question 12. The small ozone layer on top of the stratosphere is crucial for human survival. Why?

The ultraviolet rays coming from outer space are prevented by the ozone layer on top of the stratosphere from entering the inner layers of the earth’s atmosphere.

These rays are harmful to life on Earth, and the presence of the thin ozone layer is crucial for human survival.

Question 13. If the earth did not have an atmosphere, would its average surface temperature be higher or lower than what is now?

Answer:

In the absence of an atmosphere, there would be no greenhouse effect and the temperature of the earth would be lower than what it is now.

Question 14. Electromagnetic waves are produced by

1. A static charge
2. A uniformly moving charge
3. An accelerated charge
4. Neutral particle

Answer:

Electromagnetic waves are produced by accelerated charges.

The option 3 is correct.

Question 15. An electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time, \(\vec{E}\) = 6.3\(\hat{j}\) volt/meter. What is the value and direction of B of the wave at that point?

Answer:

Magnitude of magnetic field \(\vec{B}\)

∴ \(B=\frac{E}{c}=\frac{6.3}{3 \times 10^8}=2.1 \times 10^{-8} \mathrm{~Wb} \cdot \mathrm{m}^{-2}\)

The direction of wave propagation: x-axis

Direction of \(\vec{E}\): y-axis (unit vector is directed along \({j}\))

∴ \(\vec{B}\) is directed along z-axis.

∴ \(\vec{B}=\left(2.1 \times 10^{-8}\right) \hat{k} \mathrm{~Wb} \cdot \mathrm{m}^{-2}\).

Real-Life Applications of Electromagnetic Waves

Question 16. The speed of electromagnetic waves in a vacuum is

1. \(\sqrt{\epsilon_0 \mu_0}\)
2. \(\frac{1}{\sqrt{\epsilon_0 \mu_0}}\)
3. \(\epsilon_0 \mu_0\)
4. \(\frac{1}{\epsilon_0 \mu_0}\)

Answer:

2. \(\frac{1}{\sqrt{\epsilon_0 \mu_0}}\)

The option 2 is correct.

Question 17. Electromagnetic waves do not carry

1. Energy
2. Charge
3. Information
4. Momentum

Answer:

2. Charge

The option 2 is correct.

Question 18. A plane electromagnetic wave E_z = 100cos(6 x 10⁸t + 4x)V/m propagates in a medium. Find the refractive index of the medium.

Answer:

Comparing with the equation,

⇒ \(E=E_0 \cos (\omega t+k x)\)

we get, ω = 6 x 10⁸ s^-1, k = 4 m^-1

∴ The velocity of the electromagnetic wave in the medium,

⇒ \(v=\frac{\omega}{k}=\frac{6 \times 10^8}{4}=1.5 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)

The refractive index of the medium,

∴ \(\mu=\frac{c}{v}=\frac{3 \times 10^8}{1.5 \times 10^8}=2\)

Question 19. The electric and magnetic fields of electromagnetic waves are

1. In opposite phase and perpendicular to each other
2. In opposite phases and parallel to each other
3. In the same phase and perpendicular to each other
4. In the same phase and parallel to each other

Answer:

3. In the same phase and perpendicular to each other

Question 20. The speed of an electromagnetic wave in a material medium is given by \(v=\frac{1}{\sqrt{\mu \epsilon}}\), μ being the permeability of the medium and e its permittivity. How does its frequency change?

Answer:

The speed and wavelength of an em wave change when it enters a material medium, but its frequency remains unchanged.

Question 21. Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiation. Name the radiations and write the range at their frequency.

Answer:

To protect the eye from UV radiation.

Examples of Electromagnetic Wave Phenomena

Question 22. A capacitor made of two parallel plates each of plate area A and separation d is being charged by an external AC source. Show that the displacement current inside the capacitor is the same as the current charging the capacitor.

Answer:

The capacitance of the parallel plate capacitor

⇒ \(C=\frac{\epsilon_0 A}{d}\)

Effective emf in a purely capacitative circuit driven by an AC voltage V is

⇒ \(V^{\prime}=V-\frac{q}{C}\)

∴ The circuit equation is

⇒ \(V-\frac{q}{C}=0 \text { or, } q=C V\)

∴ Charging current, I = \(\frac{d q}{d t}=C \frac{d V}{d t}=\frac{\epsilon_0 A}{d} \frac{d V}{d t}\)

Displacement Current,

⇒ \(I_d=\epsilon_0 \frac{d \phi_E}{d t}=\epsilon_0 \frac{d}{d t}(E A)=\epsilon_0 \frac{d}{d t}\left(\frac{V}{d} A\right)=\frac{\epsilon_0} A \frac{d V}{d t}\)

∴ I_d = 1

Question 23. To which part of the electromagnetic spectrum does a wave of frequency 3 x 10¹³ Hz belong?

Answer:

∴ \(\lambda=\frac{c}{f}=\frac{3 \times 10^{8}}{3 \times 10^{13}}=10^{-5} \mathrm{~m}\)

This belongs to the infrared part of the electromagnetic spectrum.

Question 24. Define the intensity of radiation based on a photon picture of light. Write its SI unit.

Answer:

1st Part: The intensity of radiation is the energy transmitted in unit time through photons across a unit area normal to the photon beam.

2nd Part: Its SI unit is J.m-2. s^-1 or W. m^-2

Question 25.

1. Which one of the following electromagnetic radiations has the least frequency: UV radiations, X-rays, Microwaves
2. How do you show that electromagnetic waves carry energy and momentum?

Answer:

1. UV radiations.
2. Electromagnetic waves are streams of photon particles. Since photon particles carry both energy and momentum, electromagnetic waves also carry energy and momentum.

Question 26. How are electromagnetic waves produced? What is the source of energy of these waves? Write mathematical expressions for electric and magnetic fields on an electromagnetic wave propagating along the z-axis. Write any two important properties of electromagnetic waves.

Answer:

Electromagnetic waves are produced when charged particles oscillate. The vibrations of charged particles result in energy which is emitted as electromagnetic radiation.

The mathematical expressions for electric and magnetic fields along the z-axis are

⇒ \(\vec{E}=E_0 \sin (\omega t-k z) \hat{i} \text { and } \vec{B}=B_0 \sin (\omega t-k z) \hat{j}\)

Properties of electromagnetic waves:

1. They carry energy through space and this energy is distributed equally between the electric and magnetic fields at the time of propagation of electromagnetic waves.
2. They do not require any material medium for their propagation.

Question 27. Why does current in a steady state not flow in a capacitor connected across a battery? However momentary current does flow during the charging or discharging of the capacitor explain.

Answer:

In a steady state, no current flows in a capacitor connected across a battery because no AC voltage is applied across the capacitor.

During the charging of the capacitor, current flows from the negative plate to the positive plate. The current flows in the opposite direction during the discharging of the capacitor.

Question 28. How is the speed of EM waves in a vacuum determined by the electric and magnetic fields?

Answer:

The speed of EM waves in vacuum in terms of the electric [E₀] and magnetic field [B₀] is, \(c=\frac{E_0}{B_0}\)

Question 29. Do electromagnetic waves carry energy and momentum?

Answer:

Yes, electromagnetic waves carry energy and momentum.

Question 30. Identify the electromagnetic waves whose wavelengths vary as

1. 10^-12m < λ < 10^-8m and
2. 10^-3m < λ < 10^-1m

Answer:

1. X-rays—used in medical imaging
2. Microwaves—used in radar

Question 31. What do you understand by the statement, “electromagnetic waves transport momentum”?

Answer:

The statement “electromagnetic waves transport momentum” means that electromagnetic waves carry momentum from one place to another in a vacuum or a medium.

Important Definitions in Electromagnetic Waves

Question 32. Name the electromagnetic radiation used for

1. Water purification and
2. Eye surgery.

Answer:

1. Ultraviolet rays and
2. Ultraviolet rays

Question 33. Why are infrared waves often called heat waves? Explain.

An object absorbs infrared waves incident on it and then its temperature increases. That is why infrared waves are called heat waves.

Question 34. Electromagnetic waves are produced by

1. A static charge
2. A uniformly moving charge
3. An accelerated charge
4. Neutral particle

Answer:

3. An accelerated charge

Electromagnetic waves are produced by accelerated charges.

The option 3 is correct

Question 35. An electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time,\(\vec{E}=6.3 \hat{j}\) volt/meter. What is the value and direction of \(\vec{B}\) of the wave at that point?

Answer:

Magnitude of magnetic field \(\vec{B}\),

⇒ \(B=\frac{E}{c}=\frac{6.3}{3 \times 10^8}=2.1 \times 10^{-8} \mathrm{~Wb} \cdot \mathrm{m}^{-2}\)

Direction of wave propagation: x-axis

Direction of \(\vec{E}\): y-axis (unit vector is directed along \(\hat{j}\))

∴ \(\vec{B}\) is directed along z-axis.

∴ \(\vec{B}=\left(2.1 \times 10^{-8}\right) \hat{k} \mathrm{~Wb} \cdot \mathrm{m}^{-2}\).

Question 36. Electromagnetic waves do not carry

1. Energy
2. Charge
3. Momentum
4. Information

Answer:

2. Charge

The option 2 is correct.

Question 37. A plane electromagnetic wave E_z = 100cos(6 x 10⁸ t + 4x)V/m propagates in a medium. Find the refractive index of the medium.

Answer:

Comparing with the equation,

E = E₀ cos (ωt + kx)

we get, ω = 6 x 10⁸ s^-1, k = 4 m^-1

∴ The velocity of the electromagnetic wave in the medium,

⇒ \(v=\frac{\omega}{k}=\frac{6 \times 10^8}{4}=1.5 \times 10^8 \mathrm{~m} \cdot \mathrm{s}^{-1}\)

The refractive index of the medium,

∴ \(\mu=\frac{c}{v}=\frac{3 \times 10^8}{1.5 \times 10^8}=2\)

Question 38. The electric and magnetic fields of electromagnetic waves are

1. In opposite phase and perpendicular to each other
2. In opposite phases and parallel to each other
3. In the same phase and perpendicular to each other
4. In the same phase and parallel to each other

Answer:

3. In the same phase and perpendicular to each other

The option 3 is correct.