Introduction to Electrodynamics · Problem 11.21

Electrodynamics and Relativity — David J. Griffiths

Physics · radiation-reaction-mechanism

Problem

An electric dipole rotates at constant angular velocity ω\omega in the xyxy plane. (The charges, ±q\pm q, are at r±=±R(cos⁡ωt x^+sin⁡ωt y^)\mathbf{r}_{\pm} = \pm R(\cos\omega t\,\hat{\mathbf{x}} + \sin\omega t\,\hat{\mathbf{y}}); the magnitude of the dipole moment is p=2qRp = 2qR.) (a) Find the interaction term in the self-torque (analogous to Eq. 11.99). Assume the motion is nonrelativistic (ωR≪c\omega R \ll c). (b) Use the method of Prob. 11.20(a) to obtain the total radiation reaction torque on this system. [Answer:−μ0p2ω36πcz^.]\left[Answer: -\frac{\mu_0 p^2\omega^3}{6\pi c}\hat{\mathbf{z}}.\right] (c) Check that this result is consistent with the power radiated (Eq. 11.60).

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