PH253: key points from the last lecture

The last lecture covered a lot of ground, but in the end there are really only two main things to take away from the last lecture:

1) Accelerating charges radiate electromagnetic energy (a.k.a., light). The total radiated power P in terms of the acceleration a for a charge q is

P = \frac{q^2a^2}{6\pi\epsilon_o c^3}

This is only valid for velocities small compared to c - even though we correctly transformed the field according to relativity, we used the classical expression for acceleration. This expression is known as the Larmor formula.

2) Since accelerating charges are radiating and therefore losing energy, they also experience a 'radiation reaction' force or a recoil due to the emission of radiation. This force is analogous to viscous drag or friction, and is given by

F = \frac{q^2}{6\pi\epsilon_o c^3}\frac{d^3x}{dt^3} = \frac{q^2}{6\pi\epsilon_o c^3}\frac{da}{dt}

Again, this is valid for low speeds compared to c, and is typically called the Abraham-Lorentz force. This force is unusual in many respects - for one, it represents the charge effectively acting on itself, and it depends on the rate of change of acceleration or the third derivative of position.