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Radiation reaction

In the physics of electromagnetism, the radiation reaction is the recoil force felt by a charged object that is emitting electromagnetic radiation. It is part of the self-force of an electric charge which is the net force that a charged object's electro-magnetic field exerts on the object itself. Another part of the self-force is an addition to the object's opposition to being accelerated (inertia) due to its electrical potential energy of self-repulsion.

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The self-force felt by a composite object is composed of the self-force felt by each of its constituent particles plus the Lorentz force that each feels as a result of the fields generated by the others within the object.

The radiation reaction is proportional to the square of the object's charge times the jerk (rate of change of acceleration) which it is experiencing. It points in the direction of the jerk. So in a cyclotron where the jerk is pointing opposite to the velocity, the radiation reaction is similar to resistance in being directed opposite to the velocity of the particle.

In an antenna, it is responsible for the radiation resistance.

The formula for the radiation reaction in a vacuum in SI units is

$\vec{F} = \frac{q^2}{6 \pi \epsilon_0 c^3} \cdot \frac{d^3 \vec{r}}{{dt}^3}$

where F is the radiation reaction force, q is the electric charge, ε₀ is the electric permittivity of the vacuum, c is the speed of light, r is the position, and t is time.

References

David J. Griffiths, Introduction to Electrodynamics, Prentice-Hall, 1999 (third edition); see sections 11.2.2 and 11.2.3
Donald H. Menzel, Fundamental Formulas of Physics, 1960, Dover Publications Inc., ISBN 0-486-60595-7, vol. 1, page 345.

Category: Electromagnetic radiation