Electromagnetic waves travel in a medium at a speed of 2 × 10⁸ ms^-1. The relative permeability of the medium is 1.0. Calculate the relative permittivity.

Solution

Given,
Speed of electromagnetic waves, v = 2 $\times$ 10⁸ m/s
Relative permeability of the medium = 1
Speed of light, $C = 3 \times 10^{8} m / s$

Using the formula of speed of electromagnetic wave in a medium,
$v = \frac{1}{\sqrt{με}}$
$v = \frac{1}{\sqrt{μ_{0} μ_{r} (ε_{0} ε_{r})}}$
$v = \frac{1}{\sqrt{μ_{0} ε_{0}}} \times \frac{1}{\sqrt{μ_{r} ε_{r}}}$

Therefore,
Relative permittivity,
$ε_{r} = \frac{c^{2}}{v^{2} μ_{r}} = \frac{{(3 \times 10^{8})}^{2}}{{(2 \times 10^{8})}^{2} \times 1} = 2.25$

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Electromagnetic waves travel in a medium at a speed of 2 × 10⁸ ms^-1. The relative permeability of the medium is 1.0. Calculate the relative permittivity.