Electromagnetic Waves
Electromagnetic waves tests Maxwell idea of displacement current, the transverse field structure, the speed of light, the electromagnetic spectrum, energy density, intensity, and momentum. Questions often ask about order of the spectrum or the relation between E and B amplitudes.
Core rules and concepts
- Accelerated charges radiate electromagnetic waves. A changing electric field produces a magnetic field and vice versa; displacement current makes Ampere law consistent with changing capacitors.
- In an electromagnetic wave, E and B are perpendicular to each other and to the propagation direction. The wave is transverse.
- In vacuum, c = 1/sqrt(mu0 epsilon0) = 3.0 x 10^8 m/s. In a medium, v = 1/sqrt(mu epsilon) = c/n.
- Amplitudes obey E0/B0 = c. Average intensity is I = 1/2 epsilon0 c E0^2, also I = 1/2 B0^2/(mu0 c).
- Spectrum from long to short wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray. Visible spans about 400 nm to 700 nm.
- Electromagnetic waves carry energy and momentum; radiation pressure is I/c for absorption and 2I/c for perfect reflection.
Worked example
An electromagnetic wave in vacuum has E0 = 300 V/m. Then B0 = E0/c = 300/(3.0e8) = 1.0e-6 T. Average intensity is I = 1/2 epsilon0 c E0^2 = 0.5(8.85e-12)(3.0e8)(300^2), approximately 1.2 x 10^2 W/m^2.
Traps that cost marks
- Drawing E and B parallel rather than perpendicular.
- Saying electromagnetic waves need a medium.
- Mixing up the order of infrared and ultraviolet.
- Using peak fields without the 1/2 factor in average intensity.
- Treating displacement current as flow of real charge through a capacitor.