Using B= _0H, find the ratio E_0 H_0 for a plane electromagnetic … - Vidyadip

Question

Using $\text{B}=\mu_0\text{H},$ find the ratio $\frac{\text{E}_0}{\text{H}_0}$ 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.

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Answer

$\text{B}=\mu_0\text{H}$
$\text{H}=\frac{\text{B}}{\mu_0}$
$\frac{\text{E}_0}{\text{H}_0}=\frac{\frac{\text{B}_0}{(\mu_0\in_0\text{C})}}{\frac{\text{B}_0}{\mu_0}}=\frac{1}{\in_0\text{C}}$
$=\frac{1}{8.85\times10^{-12}\times3\times10^8}$
$=376.6\Omega=377\Omega$
$\text{Dimension}\frac{1}{\in_0\text{C}}=\frac{1}{\big[\text{LT}^{-1}\big]\big[\text{M}^{-1}\text{L}^{-3}\text{T}^{4}\text{A}^2\big]}$
$=\frac{1}{\text{M}^{-1}\text{L}^{-2}\text{T}^{3}\text{A}^2}=\text{M}^1\text{L}^2\text{T}^{-3}\text{A}^{-2}=[\text{R}]$

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