Question

Abraham lorentz formula for radiation reaction

Answer 1

Answer:

RADIATION REACTION: THE ABRAHAM-LORENTZ FORCE

Link to: physicspages home page.

To leave a comment or report an error, please use the auxiliary blog.

References: Griffiths, David J. (2007), Introduction to Electrodynamics,

3rd Edition; Pearson Education - Chapter 11, Post 19.

Post date: 12 Feb 2015.

If a charged particle accelerates, it radiates away energy. This means that

if an external force is applied to a charge, not all of the energy transferred

to the charge by the force is converted to the kinetic energy of the charge;

some of the energy is radiated away in the form of electromagnetic waves.

Looked at another way, the charge accelerates less than an uncharged par-

ticle of the same mass. From Newton’s law F = ma, the net force on the

charge must be less than the applied external force. In effect, the fields

surrounding the charge exert a ’recoil’ or reaction force on the charge.

Since the power radiated by a charge (in the non-relativistic case, any-

way) is given by the Larmor formula, we might expect that this formula

could be used to work out the reaction force, Frad. If this force acts on

the charge as it moves a distance r, the work done is Frad · r, so the rate

at which this force does work, which is the power lost to radiation, is the

time derivative of this, or Frad · v. The problem with this argument is that

the Larmor formula measures only that radiation that extends out to infinity.

The fields of a moving point charge are (with u = rˆc−v)

E(r, t) = qr

4π0 (r·u)

3

-