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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.

Electromagnetic waves can only be absorbed by matter, resulting in heating.

B.

Electromagnetic waves interact with matter through electric and magnetic fields, causing oscillations in charges.

C.

Electromagnetic waves are unaffected by the nature of atoms or molecules in the medium.

D.

Electromagnetic waves can only propagate in a vacuum and not through any material medium.
Correct Answer: B

Solution:

Electromagnetic waves interact with matter by setting charges in motion through their electric and magnetic fields, which can lead to absorption, scattering, and heating, depending on the wavelength and the nature of the atoms or molecules in the medium.

Chapter Concept:

Interaction of Electromagnetic Waves with Matter

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.

Visible light

B.

Infrared waves

C.

Ultraviolet rays

D.

Gamma rays
Correct Answer: B

Solution:

Infrared waves are absorbed by greenhouse gases, which trap heat and contribute to the greenhouse effect.

Chapter Concept:

Electromagnetic Spectrum

A.

Microwaves have a long wavelength, allowing them to penetrate dense materials.

B.

Microwaves have a short wavelength, which allows for precise detection and measurement.

C.

Microwaves are absorbed by atmospheric gases, making them ideal for communication.

D.

Microwaves travel at a slower speed than other electromagnetic waves, providing better control.
Correct Answer: B

Solution:

Microwaves have short wavelengths, which makes them suitable for radar systems as they allow for precise detection and measurement of objects.

Chapter Concept:

Microwaves

A.

250 MHz

B.

500 MHz

C.

1000 MHz

D.

2000 MHz
Correct Answer: B

Solution:

The frequency of the electromagnetic waves produced by an oscillating charge is the same as the frequency of the oscillation.

Chapter Concept:

Production of Electromagnetic Waves

A.

X-rays are produced by bombarding metal targets with high-energy electrons.

B.

X-rays have longer wavelengths than visible light.

C.

X-rays are not used in medical diagnosis due to their harmful effects.

D.

X-rays are produced by the decay of radioactive nuclei.
Correct Answer: A

Solution:

X-rays are produced by bombarding metal targets with high-energy electrons, which is why they are used in medical diagnosis and cancer treatment. However, they can damage living tissues, so overexposure must be avoided.

Chapter Concept:

X-rays

A.

Remote controls

B.

Medical therapy

C.

X-ray imaging

D.

Satellite detection
Correct Answer: C

Solution:

Infrared waves are used in remote controls, medical therapy, and satellite detection. X-ray imaging uses X-rays, which are a different part of the electromagnetic spectrum.

Chapter Concept:

Infrared Waves

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.

By stationary charges.

B.

By charges in uniform motion.

C.

By accelerated charges.

D.

By magnetic monopoles.
Correct Answer: C

Solution:

Maxwell's theory states that electromagnetic waves are produced by accelerated charges, as they generate time-varying electric and magnetic fields.

Chapter Concept:

Maxwell's Equations and Electromagnetic Waves

A.

X-rays are produced by bombarding metal targets with high-energy electrons.

B.

X-rays have longer wavelengths than visible light.

C.

X-rays are not used in medical diagnosis.

D.

X-rays do not interact with living tissues.
Correct Answer: A

Solution:

X-rays are produced by bombarding metal targets with high-energy electrons. They are used in medical diagnosis and can damage living tissues, so overexposure must be avoided.

Chapter Concept:

X-rays

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Electromagnetic Waves

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True or False

Correct Answer: True

Solution:

The equations given for the electric and magnetic fields in a plane electromagnetic wave are correct as they describe sinusoidal variations of the fields in space and time, consistent with the propagation of electromagnetic waves along the zz-axis.

Chapter Concept :

Plane Electromagnetic Wave Equations

Correct Answer: True

Solution:

The relation E0/B0=cE_0/B_0 = c is a fundamental property of electromagnetic waves in vacuum, where cc is the speed of light.

Chapter Concept :

Field Amplitude Relation in EM Waves

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 introduced the concept of displacement current to resolve an inconsistency in Ampere's law, showing that a changing electric field generates a magnetic field, which is crucial for the existence of self-sustaining electromagnetic waves.

Chapter Concept :

Symmetry Between Time-Varying Electric and Magnetic Fields

Correct Answer: True

Solution:

Maxwell introduced the concept of displacement current to address the inconsistency in Ampere's circuital law. This displacement current arises from a time-varying electric field and contributes to the magnetic field just like a conduction current, as described in the excerpts.

Chapter Concept :

Displacement Current

Correct Answer: True

Solution:

The relation ω=ck\omega = ck is a standard expression for waves, including electromagnetic waves, where ω\omega is the angular frequency, cc is the speed of light, and kk is the wave number. This relationship is derived from the wave equation and is consistent with Maxwell's equations.

Chapter Concept :

Mathematical Relations in Electromagnetic Waves

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

Correct Answer: False

Solution:

In a vacuum, electromagnetic waves are transverse waves where the oscillating electric and magnetic fields are perpendicular to each other and to the direction of wave propagation.

Chapter Concept :

Wave Propagation and Polarization

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: True

Solution:

Electromagnetic waves are self-sustaining oscillations of electric and magnetic fields that can propagate through a vacuum, unlike mechanical waves which require a medium.

Chapter Concept :

Electromagnetic Spectrum

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