Question

Mue zero and epsilen zero mai relation

Answer 1

Answer:

Explanation

Consider two charged parallel lines. They repel electrostatically by an amount determined by the field of a charged line at distance r from the center: ρ2πϵ0r, so they get pushed apart by a force f per unit length which is equal to:

fE=ρ^2/2πϵ0R

there is now a static magnetic field given by Ampere's law μ0ρ′v/2πr, and this creates a magnetic force by the Lorentz force:

fB=(μ0ρ′2/2πR)v^2

The electric and magnetic forces have to cancel as the speed of your frame approaches the speed of light, in order for the total motion to slow down as required by relativistic time dilation. This means that at v=c, the two forces must be equal and opposite, so that

μ0c^2−1/ϵ0=0

So that the relation follows from relativity.