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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.
Solution
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]`
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