Classical Electrodynamics · Problem 9.14

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · circular-loop-antenna-radiation

Problem

An antenna consists of a circular loop of wire of radius

a

located in the

x

y

plane with its center at the origin. The current in the wire is

I = I_0 \cos\omega t = \text{Re}\, I_0 e^{-i\omega t}

(a) Find the expressions for

\mathbf{E}

\mathbf{H}

in the radiation zone without approximations as to the magnitude of

ka

. Determine the power radiated per unit solid angle. (b) What is the lowest nonvanishing multipole moment (

Q_{l,m}

M_{l,m}

)? Evaluate this moment in the limit

ka \ll 1