Electromagnetic Waves Cheatsheet

Cheat Codes & Shortcuts

• Definition: Electromagnetic waves are transverse waves consisting of oscillating electric and magnetic fields.
• Wave Equation: \( \nabla^2 \mathbf{E} = \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} \), same for \( \mathbf{B} \).
• Speed of Light: \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \approx 3 \times 10^8 \, \text{m/s} \).
• Wave Speed: \( v = \frac{c}{n} \), where \( n \) is the refractive index.
• Energy Density: \( u = \frac{1}{2} \epsilon_0 E^2 + \frac{1}{2} \frac{B^2}{\mu_0} \).
• Poynting Vector: \( \mathbf{S} = \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B} \), energy flux.
• Polarization: Direction of electric field oscillation (linear, circular, elliptical).
• Maxwell’s Equations: Govern EM wave propagation in vacuum and media.
• Frequency and Wavelength: \( c = f \lambda \).
• Doppler Effect: \( f' = f \frac{c \pm v}{c} \) for moving source/observer.

Quick Reference Table

Type	Property	Formula/Description
Wave Speed	In vacuum	\( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \approx 3 \times 10^8 \, \text{m/s} \)
Energy Density	Electric + Magnetic	\( u = \frac{1}{2} \epsilon_0 E^2 + \frac{1}{2} \frac{B^2}{\mu_0} \)
Poynting Vector	Energy flow	\( \mathbf{S} = \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B} \)
Wave Equation	Electric Field	\( \nabla^2 \mathbf{E} = \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} \)
Frequency	Relation to wavelength	\( c = f \lambda \)
Polarization	Types	Linear, circular, or elliptical

Advice

Electromagnetic Waves Quick Tips

• Wave Nature: EM waves are transverse, with \( \mathbf{E} \) and \( \mathbf{B} \) perpendicular to each other and propagation direction.
• Speed in Medium: Use \( v = \frac{c}{n} \) for waves in a medium with refractive index \( n \).
• Polarization: Determine if wave is linearly or circularly polarized based on \( \mathbf{E} \)-field oscillation.
• Energy Transport: Compute Poynting vector \( \mathbf{S} \) for energy flux direction.
• Spectrum: Know the EM spectrum: radio, microwave, IR, visible, UV, X-ray, gamma.

Electromagnetic Waves Speed Quiz

Test your speed with 5 electromagnetic waves questions! You have 30 seconds per question.