Formula sheet: Electromagnetic Waves
Electromagnetic Waves10 min readLesson 1 of 5
1.1 Core formulas
| Quantity | Expression | Notes |
|---|---|---|
| Displacement current | I_d = epsilon0 d(phi_E)/dt | between the plates of a charging capacitor |
| Ampere Maxwell law | closed loop integral of B dot dl = mu0 (I_c + I_d) | I_c is the conduction current |
| Speed of electromagnetic waves in vacuum | c = 1 / square root of (mu0 epsilon0) | equals 3 x 10 to the power 8 m per second |
| Speed in a medium | v = 1 / square root of (mu epsilon) = c / square root of (mu_r epsilon_r) | mu_r and epsilon_r are relative values |
| Ratio of field amplitudes | E0 / B0 = c | E and B oscillate in phase |
| Wave number | k = 2 pi / lambda | |
| Angular frequency | omega = 2 pi nu | |
| Wave relation | c = nu lambda | also E0/B0 = c |
| Average energy density | u = half epsilon0 E0 squared | equal electric and magnetic shares |
| Intensity | I = average energy density times c | energy crossing unit area per second |
| Momentum of the wave | p = U / c | U is the energy transported |
1.2 The spectrum in order
From longest wavelength and lowest frequency to shortest and highest: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. In vacuum every one of them travels at the same speed c. The visible band runs from about 400 nm to about 700 nm, with violet at the short wavelength end and red at the long wavelength end. Infrared lies just beyond the red end and ultraviolet just beyond the violet end.
1.3 Production, detection and one use each
| Band | Produced by | Typical use |
|---|---|---|
| Radio | accelerated charges in conducting wires, oscillating circuits | radio and television communication |
| Microwaves | klystrons, magnetrons and Gunn diodes | radar, microwave oven |
| Infrared | hot bodies and molecules, vibrations of atoms | greenhouse effect, remote controls |
| Visible | electron transitions in atoms, the Sun and lamps | sight, photography |
| Ultraviolet | very hot bodies and special lamps, the Sun | sterilising, LASIK eye surgery |
| X-rays | high energy electron transitions or electron bombardment of a metal target | medical imaging, crystal structure study |
| Gamma rays | nuclear transitions and radioactive decay | cancer treatment, sterilising equipment |