Classical Electrodynamics · Problem 9.12

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · almost-spherical-surface-charge-radiation

Problem

An almost spherical surface defined by R(θ)=R0[1+βP2(cos⁡θ)]R(\theta) = R_0[1 + \beta P_2(\cos\theta)] has inside of it a uniform volume distribution of charge totaling QQ. The small parameter β\beta varies harmonically in time at frequency ω\omega. This corresponds to surface waves on a sphere. Keeping only lowest order terms in β\beta and making the long-wavelength approximation, calculate the nonvanishing multipole moments, the angular distribution of radiation, and the total power radiated.

Related theory

Browse the problem library