Electromagnetic Waves – Principles & Applications Explained | Chapter 32 of University Physics

Chapter 32 unifies electricity and magnetism into the self-sustaining phenomenon of electromagnetic waves. We’ll explore how Maxwell’s equations predict wave propagation at the speed of light, the transverse nature of E and B fields, energy and momentum transport, standing wave formation, and real-world applications from radio to lasers.

Watch the full video summary here for animated demonstrations of EM wave behavior.

Maxwell’s Equations & Wave Generation

Maxwell’s extension of Faraday’s and Ampère’s laws shows that time-varying E fields induce B fields and vice versa, forming a self-propagating wave. The wave speed in vacuum is:

c = 1/√(ε₀ μ₀) ≈ 3.00×10⁸ m/s,

matching the measured speed of light and confirming light as an electromagnetic wave.

Plane Waves & Transverse Nature

Electromagnetic waves are transverse: E and B oscillate perpendicular to each other and to the direction of travel. Their relationship is:

E = c B,

and in matter: v = 1/√(ε μ), with refractive index n = c/v.

Sinusoidal Waveforms

A plane EM wave traveling in the +x direction has fields:

• E_y(x,t) = E_max cos(kx – ωt)
• B_z(x,t) = B_max cos(kx – ωt)

Here ω = 2πf, k = 2π/λ, and c = λf. Polarization describes the orientation of E’s oscillation.

Energy & Momentum Transport

EM waves carry energy and momentum. The Poynting vector gives energy flux:

S = (1/μ₀) (E × B),

with average intensity:

I = ⟨S⟩ = ½ ε₀ c E_max².

They also exert radiation pressure:

• Absorbing surface: p_rad = I/c
• Reflecting surface: p_rad = 2I/c

Standing Electromagnetic Waves

When EM waves reflect in cavities, they form standing patterns:

• E_y = –2 E_max sin(kx) sin(ωt)
• B_z = 2 B_max cos(kx) cos(ωt)

Nodes of E align with antinodes of B. Resonant cavity modes satisfy:

• λₙ = 2L/n
• fₙ = n c/(2L)

These principles enable microwave ovens, lasers, and particle accelerators.

Conclusion

Chapter 32 reveals how Maxwell’s synthesis predicts a spectrum of electromagnetic phenomena, from radio waves to X-rays. Understanding wave propagation, energy flow, and resonance is essential for optics, communications, and advanced physics.

If you found this breakdown helpful, be sure to subscribe to Last Minute Lecture for more chapter-by-chapter textbook summaries and academic study guides.