Sources of Electromagnetic Waves

Why Are Electromagnetic Waves Produced?

Electromagnetic waves are not produced by every charge. The key condition is acceleration.

• Stationary charges produce only a static electric field ($\vec{E}$) — no wave.
• Charges in uniform motion (steady currents) produce a static magnetic field ($\vec{B}$) — still no wave, because neither field changes with time.
• Accelerated charges are the true sources. This is a central result of Maxwell's theory: only when a charge accelerates does it radiate electromagnetic energy.

How Does an Oscillating Charge Create a Wave?

Consider a charge oscillating back and forth with some frequency $f$. Because its velocity changes, it is accelerating.

1. The oscillating charge produces an oscillating electric field in the space around it.
2. This changing electric field, by Maxwell's laws, generates an oscillating magnetic field.
3. The changing magnetic field, in turn, generates a new oscillating electric field.
4. These fields regenerate each other as the disturbance travels outward.

The result is a self-sustaining electromagnetic wave. The frequency of the wave ($\nu$) is exactly equal to the frequency of oscillation of the source charge.

The energy carried by the wave comes from the kinetic energy of the accelerating charge.

Why Can't We Easily Test This for Visible Light?

The idea seems simple: make an AC circuit oscillate at the frequency of visible light (e.g., yellow light). However, this is practically impossible.

• Frequency of yellow light: $\approx 6 \times 10^{14} \text{ Hz}$
• Maximum frequency from modern electronic circuits: $\approx 10^{11} \text{ Hz}$ (radio wave region)

Because of this huge gap, the first experimental proof of electromagnetic waves had to be done at much lower frequencies — in the radio wave region.

Key Historical Experiments

• Heinrich Hertz (1887): Successfully produced and detected electromagnetic waves in the radio frequency range. This was the first direct experimental verification of Maxwell's theory. …