A rigid air-spaced coaxial cable has an inner conductor of radius and an outer…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic waves and their propagation · Electromagnetic waves and their propagation

Electricity, Magnetism and Electromagnetism, Ch Plane electromagnetic waves: polarisation, energy flux and radiation pressure

Problem

A rigid air-spaced coaxial cable has an inner conductor of radius

a = 1.20\ \mathrm{mm}

and an outer conductor whose inner radius is

b = 4.20\ \mathrm{mm}

; the space between them is vacuum. From Chapter 12, per unit length the cable has

L' = (\mu_0/2\pi)\ln(b/a)

and

C' = 2\pi\varepsilon_0/\ln(b/a)

. Take

\varepsilon_0 = 8.854\times10^{-12}\ \mathrm{F\,m^{-1}}

and

\mu_0 = 4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}

. ((a)) Compute

L'

and

C'

, and hence the speed

1/\sqrt{L'C'}

. Compare it with

1/\sqrt{\mu_0\varepsilon_0}

. ((b)) A plane electromagnetic wave in vacuum (no charges, no currents) travels along

+z

with

\mathbf{E} = E_0\cos(kz - \omega t)\hat{\mathbf{x}}

, where

E_0 = 4.0\ \mathrm{V\,m^{-1}}

and the frequency is

f = 200\ \mathrm{MHz}

. Find the wave number

k

and the magnetic field amplitude

B_0

, and state the direction of

\mathbf{B}

. ((c)) Find the intensity of this wave.

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