Undergrad Troubleshooting a Derivation: Why μ*ε=1/c^2?

Thread starter snate
Start date May 22, 2017
Tags

Derivation Electromagetism Maxwell equations Troubleshooting Wave Wave equation

Click For Summary

SUMMARY

The discussion centers on the derivation of the relationship μ*ε=1/c², which is crucial in understanding electromagnetic wave propagation. The user references a video that explains the wave equation, specifically at the 10:20 mark, where the equation v²=ω²/k² is presented. It is established that in this context, v² is equivalent to 1/(μ₀ε₀), linking the speed of light to the permeability (μ₀) and permittivity (ε₀) of free space. This relationship is fundamental in electromagnetism and wave theory.

PREREQUISITES

Understanding of electromagnetic theory
Familiarity with wave equations
Knowledge of the constants μ₀ (permeability) and ε₀ (permittivity)
Basic calculus and algebra for manipulating equations

NEXT STEPS

Study the derivation of the wave equation in detail
Learn about the physical significance of μ₀ and ε₀ in electromagnetism
Explore the implications of the speed of light in various media
Investigate the relationship between wave speed, frequency, and wavelength

USEFUL FOR

Students and professionals in physics, particularly those focused on electromagnetism and wave mechanics, as well as educators seeking to clarify these concepts for learners.

May 22, 2017

snate

I've been following the derivations in the following video up until that point. I don't quite understand why does it imply that μ*ε=1/c^2. Thanks.

Physics news on Phys.org

May 22, 2017

BvU

Science Advisor

Homework Helper

Check out the wave equation earlier on in the video (10:20) . ##v^2=\omega^2/k^2 ## and ##{1\over \mu_0\varepsilon_0}## takes that place, so ##v^2 = {1\over \mu_0\varepsilon_0}## .