Introduction to Electrodynamics · Problem 9.40

Potentials and Fields — David J. Griffiths

Physics · resonant-cavity-rectangular

Problem

Consider the resonant cavity produced by closing off the two ends of a rectangular wave guide, at

z = 0

and at

z = d

, making a perfectly conducting empty box. Show that the resonant frequencies for both TE and TM modes are given by

\omega_{lmn} = c\pi\sqrt{(l/d)^2 + (m/a)^2 + (n/b)^2}, \tag{9.204}

for integers

l

m

, and

n

. Find the associated electric and magnetic fields.