EMG-07

Maxwell wave speed

c = 1/√(μ0 ε0) in vacuum.

Reading speed

Electromagnetic wavesMaxwell 1865

Governing equation

c=\dfrac{1}{\sqrt{\mu\varepsilon}}=\dfrac{c_0}{\sqrt{\mu_r\varepsilon_r}}

where

\mu_r: Relative permeability (—)
\varepsilon_r: Relative permittivity (—)
c: Wave speed (m/s)
n: Refractive index (—)

Lecture brief

Historical brief

Coulomb, Gauss, Ampère, Faraday and Maxwell (1861–65) unified charge, current and light. The lab computes fields, induction, Poynting flux and the electromagnetic wave in SI. This sheet (EMG-07 — Maxwell wave speed) is the form associated with Maxwell 1865. Working symbols: $\mu_r$ , $\varepsilon_r$ $\rightarrow$ $c$ , $n$ . Maxwell's curl equations in free space combine into a wave equation whose speed is 1/√(με), equal to the measured speed of light.

Purpose

Purpose: compute

c

n

from

\mu_r

\varepsilon_r

in Electromagnetism via

c=\dfrac{1}{\sqrt{\mu\varepsilon}}=\dfrac{c_0}{\sqrt{\mu_r\varepsilon_r}}

c = 1/√(μ0 ε0) in vacuum. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu_r = 1.000\,\mathrm{—}

\varepsilon_r = 1.000\,\mathrm{—}

, the governing relation

c=\dfrac{1}{\sqrt{\mu\varepsilon}}=\dfrac{c_0}{\sqrt{\mu_r\varepsilon_r}}

yields

c = 3e+8\,\mathrm{m/s}

n = 1.0000\,\mathrm{—}

. Linear isotropic medium; vacuum defaults μr = εr = 1. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Relative permeability \mu_r1 —Relative permittivity \varepsilon_r1 —

Outputs

Wave speed c299792458 m/s
Refractive index n1.0000 —

Reading speed

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Narration of this film

Linear isotropic medium; vacuum defaults μr = εr = 1.

Maxwell's curl equations in free space combine into a wave equation whose speed is 1/√(με), equal to the measured speed of light.

Reading speed

Watch on YouTube