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Class 12 Science (PCM)

Physics Part 1

Electromagnetic Waves

Electromagnetic Waves

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Study Action Plan (Sorted by Difficulty)
Ampere-Maxwell Law
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Charging Capacitor and Displacement Current
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Displacement Current
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Electromagnetic Spectrum
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EM Spectrum Production and Detection Table
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Field Amplitude Relation in EM Waves
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Infrared Waves
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Interaction of Electromagnetic Waves with Matter
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Mathematical Relations in Electromagnetic Waves
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Maxwell's Equations and Electromagnetic Waves
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Maxwell’s Equations in Vacuum
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Microwaves
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Plane Electromagnetic Wave Equations
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Production of Electromagnetic Waves
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Radio Waves
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Speed of Electromagnetic Waves in Vacuum and Medium
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Symmetry Between Time-Varying Electric and Magnetic Fields
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Transverse Nature of Electromagnetic Waves
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Wave Propagation and Polarization
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X-rays
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Learning Objectives

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  • Understand the concept of electromagnetic waves and their properties.
  • Describe Maxwell's equations and their significance in electromagnetism.
  • Explain the relationship between electric and magnetic fields in electromagnetic waves.
  • Analyze the behavior of electromagnetic waves in different media.
  • Calculate the speed, frequency, and wavelength of electromagnetic waves.
  • Identify the different regions of the electromagnetic spectrum and their characteristics.
  • Apply the concepts of displacement current and its role in Ampere's circuital law.
  • Solve problems related to electromagnetic waves, including energy calculations and field amplitudes.

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Revision Notes & Summary

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Chapter Eight: Electromagnetic Waves

8.1 Introduction

  • Electric current produces a magnetic field.
  • A time-varying electric field generates a magnetic field.
  • Maxwell introduced the concept of displacement current to resolve inconsistencies in Ampere's law.
  • Maxwell's equations describe the relationship between electric and magnetic fields.
  • Prediction of electromagnetic waves: coupled time-varying electric and magnetic fields that propagate in space.

8.3 Key Concepts

  • Electromagnetic Wave Characteristics:
    • All electromagnetic waves travel at the same speed in vacuum.
    • Different types of electromagnetic waves differ in wavelength and frequency.
    • Accelerated charged particles radiate electromagnetic waves.
    • Wavelength correlates with the size of the radiating system.
  • Types of Electromagnetic Waves:
    • Gamma rays: 10⁻¹⁴ m to 10⁻¹⁵ m (from atomic nuclei)
    • X-rays: emitted from heavy atoms
    • Radio waves: produced by accelerating electrons in circuits
    • Infrared waves: increase internal energy and temperature of substances

8.4 Electromagnetic Spectrum

  • The electromagnetic spectrum includes:
    • Gamma rays
    • X-rays
    • Ultraviolet rays
    • Visible rays
    • Infrared rays
    • Microwaves
    • Radio waves
  • Classification based on frequency and production/detection methods.

Examples

  • Example 8.1: A plane electromagnetic wave of frequency 25 MHz has an electric field E = 6.3 j V/m. To find B:
    • Direction of B is perpendicular to both E and the direction of wave propagation.
  • Example 8.2: Given a magnetic field By = (2 x 10⁻⁷) T sin (0.5 x 10³x + 1.5 x 10¹¹t):
    • Determine wavelength and frequency.
    • Write expression for electric field.

Important Notes

  • The speed of electromagnetic waves in vacuum is the speed of light, c = 3 x 10⁸ m/s.
  • The relationship between electric field (E) and magnetic field (B) in a wave is given by E₀/B₀ = c.
  • The average energy density of the electric field equals that of the magnetic field.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

c=1ε0μ0c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}

B.

c=ε0μ0c = \varepsilon_0 \mu_0

C.

c=ε0μ0c = \sqrt{\varepsilon_0 \mu_0}

D.

c=ε0+μ0c = \varepsilon_0 + \mu_0
Correct Answer: A

Solution:

The speed of light cc in vacuum is given by the relation c=1ε0μ0c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}, where ε0\varepsilon_0 is the permittivity and μ0\mu_0 is the permeability of free space.

Chapter Concept:

Maxwell's Equations and Electromagnetic Waves

A.

Both vectors are parallel to the direction of wave propagation.

B.

The electric field vector is perpendicular to the magnetic field vector, and both are perpendicular to the direction of wave propagation.

C.

The electric field vector is parallel to the wave propagation, while the magnetic field vector is perpendicular.

D.

Both vectors are antiparallel to the direction of wave propagation.
Correct Answer: B

Solution:

In a plane electromagnetic wave traveling in vacuum, the electric and magnetic field vectors are perpendicular to each other and to the direction of wave propagation, which is characteristic of transverse waves.

Chapter Concept:

Speed of Electromagnetic Waves in Vacuum and Medium

A.

Conduction current

B.

Displacement current

C.

Magnetic flux

D.

Electric potential
Correct Answer: B

Solution:

Maxwell introduced the concept of displacement current to account for the time-varying electric field, which is given by id=ε0dΦEdti_d = \varepsilon_0 \frac{d\Phi_E}{dt}.

Chapter Concept:

Ampere-Maxwell Law

A.

0 A

B.

0.1 A

C.

0.2 A

D.

0.4 A
Correct Answer: C

Solution:

The displacement current between the plates of a charging capacitor is equal in magnitude to the conduction current in the wires, which is 0.2 A.

Chapter Concept:

Charging Capacitor and Displacement Current

A.

Stationary charges produce electromagnetic waves.

B.

Charges in uniform motion produce electromagnetic waves.

C.

Accelerated charges produce electromagnetic waves.

D.

Electromagnetic waves are produced by magnetic monopoles.
Correct Answer: C

Solution:

Accelerated charges radiate electromagnetic waves. This is a fundamental result of Maxwell's theory.

Chapter Concept:

Production of Electromagnetic Waves

A.

530 kHz to 1710 kHz

B.

54 MHz to 890 MHz

C.

88 MHz to 108 MHz

D.

500 kHz to 1000 MHz
Correct Answer: C

Solution:

The FM radio band extends from 88 MHz to 108 MHz.

Chapter Concept:

Radio Waves

A.

They have the highest frequency in the electromagnetic spectrum.

B.

They are absorbed by water molecules, increasing thermal motion.

C.

They are visible to the human eye.

D.

They are produced by nuclear reactions.
Correct Answer: B

Solution:

Infrared waves are absorbed by water molecules, which increases their thermal motion, thus raising the temperature.

Chapter Concept:

Electromagnetic Spectrum

A.

By=B0cos⁡(kz−ωt)B_y = B_0 \cos(kz - \omega t)

B.

By=B0sin⁡(kz−ωt)B_y = B_0 \sin(kz - \omega t)

C.

By=B0sin⁡(kz+ωt)B_y = B_0 \sin(kz + \omega t)

D.

By=B0cos⁡(kz+ωt)B_y = B_0 \cos(kz + \omega t)
Correct Answer: B

Solution:

For a plane electromagnetic wave propagating along the z-axis, the electric and magnetic fields are in phase. Therefore, By=B0sin⁡(kz−ωt)B_y = B_0 \sin(kz - \omega t) is the correct expression.

Chapter Concept:

Plane Electromagnetic Wave Equations

A.

UV radiation has long wavelengths that penetrate deep into the skin.

B.

UV radiation is absorbed by melanin, increasing its production.

C.

UV radiation has high energy that can break chemical bonds in skin cells.

D.

UV radiation is reflected by the skin, causing heat damage.
Correct Answer: C

Solution:

UV radiation has high energy due to its short wavelength, which can break chemical bonds in skin cells, leading to tanning and potential damage.

Chapter Concept:

Electromagnetic Spectrum

A.

4.0×10−7 T4.0 \times 10^{-7} \text{ T}

B.

4.0×10−8 T4.0 \times 10^{-8} \text{ T}

C.

3.0×10−8 T3.0 \times 10^{-8} \text{ T}

D.

3.0×10−7 T3.0 \times 10^{-7} \text{ T}
Correct Answer: B

Solution:

The amplitude of the magnetic field is given by B0=E0cB_0 = \frac{E_0}{c}, where c=3×108 m/sc = 3 \times 10^8 \text{ m/s}. Substituting the given values, B0=1203×108=4.0×10−8 TB_0 = \frac{120}{3 \times 10^8} = 4.0 \times 10^{-8} \text{ T}.

Chapter Concept:

Transverse Nature of Electromagnetic Waves

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True or False

Correct Answer: True

Solution:

Electromagnetic waves in a vacuum indeed travel at the speed c=1μ0ε0c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}, where μ0\mu_0 is the permeability of free space and ε0\varepsilon_0 is the permittivity of free space. The ratio of the magnitudes of the electric field E0E_0 and the magnetic field B0B_0 is equal to the speed of light cc.

Chapter Concept :

Wave Propagation and Polarization

Correct Answer: True

Solution:

Maxwell's equations, by predicting the existence of electromagnetic waves, showed that light is an electromagnetic wave, thereby unifying the domains of electricity, magnetism, and optics.

Chapter Concept :

Maxwell's Equations and Electromagnetic Waves

Correct Answer: True

Solution:

Maxwell's equations describe how time-varying electric fields can generate magnetic fields, which is a fundamental principle leading to the existence of electromagnetic waves. This is supported by the Ampere-Maxwell law, which includes the displacement current term.

Chapter Concept :

Maxwell’s Equations in Vacuum

Correct Answer: True

Solution:

According to Maxwell's equations, the speed of electromagnetic waves in a vacuum is c=1μ0ϵ0=3×108c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8 m/s, and this speed is uniform for all electromagnetic waves in a vacuum.

Chapter Concept :

Speed of Electromagnetic Waves in Vacuum and Medium

Correct Answer: True

Solution:

Maxwell introduced the concept of displacement current, id=ε0dΦEdti_d = \varepsilon_0 \frac{d\Phi_E}{dt}, to address the inconsistency in Ampere's circuital law when applied to a charging capacitor. This displacement current accounts for the time-varying electric field that produces a magnetic field similar to conduction current.

Chapter Concept :

Displacement Current

Correct Answer: True

Solution:

Electromagnetic waves interact with matter by inducing oscillations in charges due to their electric and magnetic fields, leading to phenomena such as absorption, scattering, and heating.

Chapter Concept :

Interaction of Electromagnetic Waves with Matter

Correct Answer: True

Solution:

Electromagnetic waves are self-sustaining oscillations of electric and magnetic fields and do not require a material medium to propagate. This is a fundamental characteristic of electromagnetic waves, as described by Maxwell's equations.

Chapter Concept :

Interaction of Electromagnetic Waves with Matter

Correct Answer: True

Solution:

Electromagnetic waves are transverse waves where the electric field EE and the magnetic field BB oscillate perpendicular to each other and to the direction of propagation, as described by Maxwell's equations.

Chapter Concept :

Mathematical Relations in Electromagnetic Waves

Correct Answer: False

Solution:

The electromagnetic spectrum does include radio waves, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays, but the boundaries between these regions are not sharply defined. They differ mainly in production, detection, and interaction with matter.

Chapter Concept :

Electromagnetic Spectrum

Correct Answer: True

Solution:

In a plane electromagnetic wave, the electric field (EE) and magnetic field (BB) oscillate sinusoidally and are perpendicular to each other as well as to the direction of wave propagation. This is a fundamental characteristic of electromagnetic waves, confirming their transverse nature.

Chapter Concept :

Transverse Nature of Electromagnetic Waves

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