 Radiation damping of a harmonically oscillating charge

ID: radiation-damping-of-a-harmonically-oscillating-charge

A charge

q

ω

and slowly varying amplitude

A

radiates the averaged power

⟨ P ⟩ = \frac{μ _{0} q ^{2} A ^{2} ω ^{4}}{12 π c} .

E = m A^{2} ω^{2} /2

therefore has exponential decay rate

γ = μ_{0} q^{2} ω^{2} / (6 πm c)

t_{1/2} = \frac{6 πm c l o g 2}{μ _{0} q ^{2} ω ^{2}} .

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