Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.8

Radiation of Electromagnetic Waves

Physics — Landau & Lifshitz · radiation-antenna

Problem

A half-wave antenna consists of a thin conducting wire of length

\lambda/2

driven at its center. The current distribution is

I(z, t) = I_0 \cos(kz)\cos(\omega t)

, where

k = 2\pi/\lambda

. (a) Find

dP/d\Omega

for this antenna. (b) Show that the total radiated power is

P = \frac{\mu_0 c I_0^2}{8\pi} \times 2.44

(approximately).