Electromagnetic Waves

8.1 Introduction

In Chapter 4, we learnt that an electric current produces magnetic field and that two current-carrying wires exert a magnetic force on each other. Further, in Chapter 6, we have seen that a magnetic field changing with time gives rise to an electric field. James Clerk Maxwell argued that the converse is also true — an electric field changing with time gives rise to a magnetic field.

8.2 Maxwell's Equations

Maxwell's equations are the four fundamental equations that describe all classical electromagnetism:

Figure 8.1 — EM wave structure, Maxwell's equations, and the electromagnetic spectrum

• ∇·E = ρ/ε₀ — Gauss's law for electricity
• ∇·B = 0 — Gauss's law for magnetism (no magnetic monopoles)
• ∇×E = −∂B/∂t — Faraday's law of electromagnetic induction
• ∇×B = μ₀J + μ₀ε₀∂E/∂t — Ampere-Maxwell law

8.3 Displacement Current

Maxwell introduced the concept of displacement current (I_d = ε₀dΦ_E/dt) to complete Ampere's law. This term accounts for the magnetic field produced by a changing electric field, even in the absence of conduction current.

8.4 Electromagnetic Waves

An electromagnetic wave is a self-propagating wave of oscillating electric and magnetic fields. The changing electric field creates a magnetic field, and the changing magnetic field creates an electric field — sustaining the wave indefinitely through space.

8.5 Properties of EM Waves

• E and B are perpendicular to each other and to the direction of propagation
• EM waves are transverse waves (both E and B are transverse)
• They can travel through vacuum (no medium required)
• They carry energy: energy density = ε₀E² = B²/μ₀
• They carry momentum and exert radiation pressure
• E₀/B₀ = c (amplitudes of E and B fields are related by c)

8.6 Electromagnetic Spectrum

The electromagnetic spectrum is the complete range of electromagnetic wave frequencies and wavelengths:

8.7 Applications of EM Waves