---
title: "Radiation from an Accelerating Charge"
description: "A charge that accelerates radiates power growing with the square of the acceleration, and it radiates sideways rather than along its motion. Antennas, synchrotron light and the reddening of a setting "
canonical: https://lightmysky.com/learn/science/radiation-from-an-accelerating-charge-mt_Qr0rMEOYAg
source: https://lightmysky.com/learn/science/radiation-from-an-accelerating-charge-mt_Qr0rMEOYAg.md
retrieved: 2026-09-12
---

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# Radiation from an Accelerating Charge

A charge that accelerates radiates power growing with the square of the acceleration, and it radiates sideways rather than along its motion. Antennas, synchrotron light and the reddening of a setting sun all rest on this result.

Subject: Science · Area: Electricity & Magnetism · Ages 23 to 24
Page: https://lightmysky.com/learn/science/radiation-from-an-accelerating-charge-mt_Qr0rMEOYAg

## Ready when they can

- States how radiated power depends on charge and acceleration
- Describes the angular pattern of the radiation and the direction in which it vanishes
- Applies the result to one named laboratory or astronomical source

## Lesson: Why accelerating charges glow

A charge that accelerates radiates, and a charge sitting still or gliding at steady speed stays quiet. Whenever a charged particle changes its motion it sends ripples through the fields around it, and light is one form of that radiation, including the sunlight whose warmth you felt as intensity. Color follows wavelength through c = lambda times f.

**Example.** Radiated power grows with charge squared times acceleration squared. Double the acceleration and the output quadruples; double the charge with the same motion and it quadruples too. That square law is why gentle bends whisper while violent bends blaze.

The radiation also has a shape: strongest sideways to the acceleration and zero along the line of acceleration. Picture a doughnut around the acceleration arrow with a hole on the axis. Antennas exploit this by pushing electrons back and forth so they keep accelerating.

Synchrotron radiation is this physics at near light speed: magnets bend fast electrons and the curve forces radiation. It pours from the Crab Nebula, galaxy jets, and black hole regions, and lab synchrotrons harvest it to study materials. Electron rings suffer far worse than proton rings, since lighter mass needs far bigger bending acceleration.

**Recap.** Only changing motion radiates, power follows the squared law sideways, and bent near-light electrons are the brightest sources.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Gauge Freedom and the Potentials as the Working Variables](https://lightmysky.com/learn/science/gauge-freedom-and-the-potentials-as-the-working-variables-mt_BovDzq3WZm)
- [The Poynting Vector and Radiation Pressure](https://lightmysky.com/learn/science/the-poynting-vector-and-radiation-pressure-mt_dwTbNlzBgE)

## Opens up

- [Tensors and the Metric on a Curved Manifold](https://lightmysky.com/learn/science/tensors-and-the-metric-on-a-curved-manifold-mt_9r9SG3NcZR)
- [Linearised Gravity and Gravitational Waves](https://lightmysky.com/learn/science/linearised-gravity-and-gravitational-waves-mt_z0tMZDGMHi)