Radiation from an Accelerating Charge
A charge that accelerates radiates power growing with the square of the acceleration, and it radiates sideways to its acceleration rather than along it. Antennas, synchrotron light and the reddening of a setting sun all rest on this result.
What a learner can do afterwards
- 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
1 · Read
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. Light, sunlight included, is one form of that radiation. Color follows wavelength through c = lambda times f.
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 sharp bends radiate far more than gentle ones. This power is the Poynting flux summed over a large sphere around the charge.
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. An antenna pushes electrons back and forth so they keep accelerating and keep radiating.
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 regions near black holes, and lab synchrotrons use it to study materials. Electrons also lose more energy this way than protons. At the same speed in the same field the magnetic force is the same, but a particle about 1800 times lighter gets a far larger acceleration, and power grows with acceleration squared.
Only changing motion radiates, power follows the squared law sideways, and bent near-light electrons are the brightest sources.
The rewritten readings were written for this dataset.
2 · Watch
En anglaisTake it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.