Classical Electrodynamics · Problem 9.8

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · angular-momentum-radiation-electric-dipole

Problem

(a) Show that a classical oscillating electric dipole

\mathbf{p}

with fields given by (9.18) radiates electromagnetic angular momentum to infinity at the rate

\frac{d\mathbf{L}}{dt} = \frac{k^3}{12\pi\epsilon_0}\, \text{Im}[\mathbf{p}^* \times \mathbf{p}]

(b) What is the ratio of angular momentum radiated to energy radiated? Interpret. (c) For a charge

e

rotating in the

x

y

plane at radius

a

and angular speed

\omega

, show that there is only a

z

component of radiated angular momentum with magnitude

dL_z/dt = e^2 k^3 a^2 / 6\pi\epsilon_0

. What about a charge oscillating along the

z

axis? (d) What are the results corresponding to parts a and b for magnetic dipole radiation? Hint: The electromagnetic angular momentum density comes from more than the transverse (radiation zone) components of the fields.

Related theory

Electric Dipole Radiation

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