Classical Electrodynamics · Problem 8.6

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · cylindrical-resonant-cavity

Problem

A resonant cavity of copper consists of a hollow, right circular cylinder of inner radius

R

and length

L

, with flat end faces. (a) Determine the resonant frequencies of the cavity for all types of waves. With

(1/\sqrt{\mu\epsilon}\, R)

as a unit of frequency, plot the lowest four resonant frequencies of each type as a function of

R/L

for

0 < R/L < 2

. Does the same mode have the lowest frequency for all

R/L

? (b) If

R = 2

cm,

L = 3

cm, and the cavity is made of pure copper, what is the numerical value of

Q

for the lowest resonant mode?