Question

Using B = µ₀ H, find the ratio E₀/H₀ for a plane electromagnetic wave propagating through vacuum. Show that it has the dimensions of electric resistance. This ratio is a universal constant called the impedance of free space.

Answer 1

Given, B = µ₀H

For vacuum we can rewrite this equation as,

B₀ = µ₀H₀   ...(i)
Relation between magnetic field and electric field for vacuum is given as,
`B_0 = u_0∈_0cE_0` ...(ii)

From equation (i) by (ii),

`u_0H_0 = u_0∈_0cE_0`

⇒ `E_0/H_0 = 1/(∈_0c)`

⇒ `E_0/H_0 = 1/(8.85 xx 10^-12 xx 3 xx 10^8)`

⇒ `E_0/H_0 ≈ 377  Ω`

Dimension of `1/(∈_0c) = 1/([LT^-1][M^-1L^-3T^4A^2]`

= `1/(M^-1L^-2T^3A^2)`

= `M^4L^2T^-3A^-2` = `[R]`