In The Electromagnetic Spectrum you met the family of light, from radio to gamma rays. Now we can say what light is. Faraday's Law says a changing magnetic field makes an electric field. In the 1860s James Clerk Maxwell found the partner: a changing electric field makes a magnetic field. Each one keeps making the other, and the pair travels away as a wave.
Key idea
An electromagnetic wave is linked electric and magnetic fields, at right angles to each other and to the direction of travel, rising and falling together, with $E = cB$. In a vacuum every EM wave moves at $c = 3.00 \times 10^{8}\ \text{m/s}$, and $c = f\lambda$. No medium is needed.
Why it works
Maxwell computed the speed of such a wave from two constants measured on lab benches with charges and currents, $c = 1/\sqrt{\mu_0\varepsilon_0}$, and got the measured speed of light. That match was the clue that light is an electromagnetic wave. Any accelerating charge makes these waves: electrons sloshing in a radio antenna, or jumping in an atom. The wave's electric part is the same kind of field as in The Electric Field: it pushes on charges, which is how a receiving antenna picks up the signal.
Common mistake
Two common mix-ups. (1) Thinking EM waves need a medium. Sunlight crosses $150$ million km of nearly empty space. (2) Thinking radio waves are a kind of sound. Sound is a pressure wave in matter at about $343\ \text{m/s}$; radio is light at $3.00 \times 10^{8}\ \text{m/s}$. A radio turns the radio wave into sound with its speaker.
Worked example: An FM station
An FM station broadcasts at $100\ \text{MHz}$. Find the wavelength.
- $\lambda = \dfrac{c}{f} = \dfrac{3.00 \times 10^{8}\ \text{m/s}}{100 \times 10^{6}\ \text{Hz}}$.
- $\lambda = 3.00\ \text{m}$, about the length of a car.
Answer: $3.00\ \text{m}$
Worked example: The magnetic part
An EM wave has an electric field amplitude of $30\ \text{V/m}$. Find its magnetic field amplitude.
- $B = \dfrac{E}{c} = \dfrac{30}{3.00 \times 10^{8}}$.
- $B = 1.0 \times 10^{-7}\ \text{T}$. Tiny, but it moves in step with $E$.
Answer: $1.0 \times 10^{-7}\ \text{T}$