CBSE Class 12 Physics Electromagnetic Waves Frequently Asked Questions

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PHYSICS
UNIT V
ELECTROMAGNETIC WAVES

2 MARKS

1. A plane monochromatic light wave lies in the visible region. It is represented by sinusoidal variation with time by the following components of electric field:
E_x = 0, E_y = 4 sin [\( \frac{2\pi}{\lambda} \)(x - Vt)], E_z = 0
Where, ν (freq) = 5 x 10¹⁴ Hz and ν is velocity.
(i) What is the direction of propagation of the wave?
(ii) What is its amplitude? And
(iii) Compute the components of magnetic field. [2 Marks]

Answer:
1. The electric field depends on (x - Vt), so the wave travels along the positive x-direction.
2. The amplitude of the electric field is E₀ = 4 N C^-1 (or V m^-1).
3. The magnetic field is perpendicular to both the electric field (along y) and the direction of propagation (along x), so it is along the z-direction.
4. The magnetic amplitude is B₀ = \( \frac{E_0}{c} \) = \( \frac{4}{3 \times 10^{8}} \) = \( \frac{4}{3} \) x 10^-8 T.
5. So B_x = 0, B_y = 0 and B_z = \( \frac{4}{3} \) x 10^-8 sin [\( \frac{2\pi}{\lambda} \)(x - Vt)] T, where V = c.

Teacher's Note:
a) The sign (x - Vt) tells the direction of propagation; a plus sign would mean the wave travels backwards.
b) In an electromagnetic wave, E and B are in phase and their amplitudes are related by E₀ = cB₀.

2. Give two characteristics of electromagnetic waves. Write the expression for the velocity of electromagnetic waves in terms of permittivity and magnetic permeability of free space. [2 Marks]

Answer:
1. Electromagnetic waves are transverse in nature, because the electric and magnetic fields oscillate perpendicular to the direction of propagation.
2. Electromagnetic waves do not need a material medium and travel in vacuum with the speed of light.
3. The velocity of electromagnetic waves in free space is v = \( \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \), where ε₀ is the permittivity and μ₀ is the magnetic permeability of free space.

Teacher's Note:
a) Transverse nature is the first property to write, because it is asked most often.
b) Substituting the values of ε₀ and μ₀ gives v ≈ 3 x 10⁸ m s⁻¹.

3. Find wavelength of electromagnetic waves of frequency 5 x 10¹⁹ Hz in free space. Give its two applications. [2 Marks]

Answer:
1. Given: frequency ν = 5 x 10¹⁹ Hz, speed in free space c = 3 x 10⁸ m s^-1.
2. Wavelength λ = \( \frac{c}{\nu} \) = \( \frac{3 \times 10^{8}}{5 \times 10^{19}} \) m = 6 x 10^-12 m.
3. These waves are gamma rays.
4. Two applications: gamma rays are used in the treatment of cancer (radiotherapy) and in the sterilisation of medical equipment and food.

Teacher's Note:
a) Use λ = c / ν, not ν / c, to avoid a wrong order of magnitude.
b) A wavelength of about 6 x 10⁻¹² m lies in the gamma-ray region of the spectrum.

4. Name the characteristics of e. m. waves that: (i) increases, & (ii) remains constant in e. m. spectrum as one moves from radiowave region towards ultraviolet region. [2 Marks]

Answer:
(i) Frequency (and the energy of the photons) increases.
(ii) The speed of electromagnetic waves in vacuum remains constant (3 x 10⁸ m s^-1).

Teacher's Note:
a) As we move from radio waves to ultraviolet, the wavelength decreases while the frequency increases.
b) The speed in vacuum is the same for all electromagnetic waves, whatever their frequency.

3 MARKS

5. Which constituent radiation of electromagnetic spectrum is used: (i) in radar? (ii) To photograph internal parts of human body? & (iii) for taking photographs of the sky during night and foggy condition? Give one reason for your answer in each case. [3 Marks]

Answer:
1. (i) Radar uses microwaves. Reason: their short wavelength gives a sharp reflected signal from objects, which helps in locating them.
2. (ii) X-rays are used to photograph internal parts of the body. Reason: they pass easily through soft tissues but are absorbed by bones.
3. (iii) Infrared radiation is used for photographs of the sky at night and in fog. Reason: its longer wavelength is less scattered by fog and haze.

Teacher's Note:
a) Radar needs waves that reflect well from small targets, and microwaves are suitable for this.
b) X-rays are absorbed more by denser materials such as bone, which makes the image clear.
c) Infrared photography also works in darkness, because the sky and objects emit infrared radiation.

6. Write any four characteristics of e. m. waves. Give two uses of: (i) Radio waves & (ii) Microwaves. [3 Marks]

Answer:
1. Electromagnetic waves are transverse in nature.
2. They travel in vacuum with the speed of light, 3 x 10⁸ m s^-1.
3. They do not need any material medium for propagation.
4. The electric and magnetic fields are in phase and perpendicular to each other and to the direction of propagation.
5. Uses of radio waves: (a) radio and television broadcasting, (b) mobile phone and wireless communication.
6. Uses of microwaves: (a) radar, (b) microwave ovens or satellite communication.

Teacher's Note:
a) The four characteristics asked here are the ones in the textbook list; any four of them are acceptable.
b) Radio waves have long wavelengths, which allows them to travel long distances.
c) Microwaves are short-wavelength radio waves, so they can be focused into narrow beams.

7. Name the following constituent radiations of e. m. spectrum which, (i) produce intense heating effect? (ii) is absorbed by the ozone layer, &(iii) is used for studying crystal structure. [3 Marks]

Answer:
1. (i) Infrared radiation produces an intense heating effect.
2. (ii) Ultraviolet radiation is absorbed by the ozone layer.
3. (iii) X-rays are used for studying crystal structure.

Teacher's Note:
a) Infrared waves are absorbed by matter as heat, which is why they are called heat waves.
b) The ozone layer absorbs most of the harmful ultraviolet radiation from sunlight.
c) X-ray diffraction from crystals gives information about the arrangement of atoms.

8. Experimental observations have shown: (i) that X-rays travel in vacuum with a speed of 3 x 10⁸ m s^-1, & (ii) the phenomenon of diffraction and can be polarized. What conclusion is drawn about the nature of X-rays from each of these observations? [3 Marks]

Answer:
1. From observation (i): X-rays travel in vacuum at the speed of light, so X-rays are electromagnetic waves.
2. From observation (ii): diffraction shows that X-rays have wave nature.
3. Polarisation is possible only for transverse waves, so X-rays are transverse electromagnetic waves.

Teacher's Note:
a) Only electromagnetic waves travel at the speed of light in vacuum.
b) Polarisation is a property that only transverse waves show, which is the key point of this question.
c) Diffraction is shown by all waves, so it tells us about the wave nature of X-rays but not their direction of vibration.

9. Why are infrared radiations referred to as heat waves? Name the radiations which are next to these radiations in e. m. spectrum having: (i) shorter wavelength, & (ii) longer wavelength. [3 Marks]

Answer:
1. Infrared radiation is emitted by hot bodies, and when it is absorbed by a body, it increases the body's temperature. For this reason it is called heat waves.
2. (i) The radiation next to infrared with shorter wavelength is visible light.
3. (ii) The radiation next to infrared with longer wavelength is microwave radiation.

Teacher's Note:
a) The order of the spectrum is radio, microwave, infrared, visible, ultraviolet, X-ray and gamma ray.
b) Infrared is felt as warmth on the skin, which is why it is called heat.
c) Do not confuse the direction: shorter wavelength means towards visible light, and longer wavelength means towards microwaves.

10. The oscillating magnetic field in a plane electromagnetic wave is given by:
B_y = 8 x 10^-6 sin [2 x 10¹¹ t + 300 π x] T
(i) Calculate the wavelength of the electromagnetic wave &
(ii) Write down the expression for oscillating electric filed. [3 Marks]

Answer:
1. Comparing with B = B₀ sin (ωt + kx), we get ω = 2 x 10¹¹ rad s^-1 and k = 300π m^-1.
2. Wavelength λ = \( \frac{2\pi}{k} \) = \( \frac{2\pi}{300\pi} \) = \( \frac{1}{150} \) m = 6.67 x 10^-3 m.
3. The phase is (ωt + kx), so the wave travels along the negative x-direction, and the electric field is along the z-direction.
4. Amplitude of the electric field: E₀ = cB₀ = 3 x 10⁸ x 8 x 10^-6 = 2400 V m^-1.
5. So E_z = 2.4 x 10³ sin [2 x 10¹¹ t + 300 π x] V m^-1, with E_x = 0 and E_y = 0.

Teacher's Note:
a) The wave number k is the coefficient of x in the phase, and λ = 2π / k.
b) The given values give ω / k of about 2.1 x 10⁸ m s⁻¹, which is slightly different from c; the question is meant as a direct calculation.
c) E and B are in phase, and the direction of E is found from the direction of propagation.

11. Identify the following electromagnetic radiation as per the wavelengths given below: (a) 10^-3 nm, & (b) 10^-3 m, & (c) 1 nm; Write one application of each. [3 Marks]

Answer:
1. (a) 10^-3 nm = 10^-12 m, which is in the gamma-ray region. Application: treatment of cancer.
2. (b) 10^-3 m = 1 mm, which is in the microwave region. Application: radar or microwave ovens.
3. (c) 1 nm = 10^-9 m, which is in the X-ray region. Application: medical imaging or study of crystal structure.

Teacher's Note:
a) Convert all wavelengths to metres before comparing them with the spectrum ranges.
b) 1 nm is at the lower end of the X-ray range, not the ultraviolet range.
c) Gamma rays have the shortest wavelengths in the spectrum.

12. Name the constituent radiation of electromagnetic spectrum which (a) is used in satellite communication. (b) is used for studying crystal structure. (c) is similar to the radiations emitted during decay of radioactive nuclei. (d) has its wavelength range between 390 nm and 770 nm. (e) is absorbed from sunlight by ozone layer. (f) produces intense heating effect. [3 Marks]

Answer:
1. (a) Microwaves.
2. (b) X-rays.
3. (c) Gamma rays.
4. (d) Visible light.
5. (e) Ultraviolet radiation.
6. (f) Infrared radiation.

Teacher's Note:
a) Satellite communication uses microwaves, which pass through the atmosphere.
b) Gamma rays are emitted by nuclei during radioactive decay, so they are similar to these radiations.
c) The wavelength range 390 nm to 770 nm is the range of visible light.

13. What is meant by the transverse nature of electromagnetic waves? Draw diagram showing the propagation of the an electromagnetic wave along X direction, indicating clearly the directions of oscillating electric and magnetic fields associated with it. [3 Marks]

Answer:
1. In an electromagnetic wave, the electric field and the magnetic field oscillate perpendicular to each other and also perpendicular to the direction of propagation. This is called the transverse nature of electromagnetic waves.
2. The diagram shows the wave travelling along the X-axis.
3. The electric field E oscillates along the Y-axis and the magnetic field B oscillates along the Z-axis.
4. Both fields are in phase, and the arrow of propagation points along the positive X-axis.

[Figure: diagram to be added. Arrow labelled X showing the direction of propagation. Sine wave labelled E (electric field) oscillating along the Y-axis. Sine wave labelled B (magnetic field) oscillating along the Z-axis, at right angles to E and to the X-axis.]

Teacher's Note:
a) Transverse means the oscillations are at right angles to the direction of travel.
b) E, B and the direction of propagation form three mutually perpendicular directions.
c) Polarisation is possible because of this transverse nature.

E_x = 0₁, E_y = 4 sin [2π/λ (x – Vt)], Ez = 0 X Y Where, v (freq) = 5 x 10¹⁴ H₂ and n is velocity. z