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 Incoming links: Transverse electric mode

Past exam of the physics B course of the University of Cambridge / 2010 / Paper 2A / Section A / 3 / Solution 2026-10-20

An empty perfectly conducting rectangular electromagnetic waveguide has

ω^{2} = c^{2} [k_{z}^{2} + π^{2} (\frac{m ^{2}}{a ^{2}} + \frac{n ^{2}}{b ^{2}})] .

The lowest transverse electric mode has indices

(1, 0)

or

(0, 1)

. A simply connected hollow metallic guide has no transverse electromagnetic mode. With

a = b = 1 0^{- 2} m

, the two lowest modes are degenerate and their cutoff frequency is

f_{c} = \frac{c}{2 a} ≃ 15.0 GHz .

Propagation with nonzero axial energy transport requires

f > f_{c}

; the equality is the lower limiting frequency, with zero axial group velocity. A filling medium would replace

c

by

1/ μ ϵ

.

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Past exam of the physics B course of the University of Cambridge / 2010 / Paper 2B / Section A / 3 / Solution 2026-10-20

The lowest transverse electric mode has cutoff frequency

c / (2 a) ≃ 15.0 GHz

; propagation requires frequency strictly above cutoff.

Full derivation: solution.

 Read the full article