• 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.

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.