Electromagnetic waves travel in a medium at a speed of $1.5 × 10^8 m/s$. The relative permeability of the medium is 0.4. The relative permittivity of the medium will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10
Speed of electromagnetic waves in a medium ($v$) is related to the permeability ($μ$) and permittivity ($ε$) of the medium by equation -
$v=\frac{1}{\sqrt{με}}$
Permeability, $μ=μ_0μ_r$
Permittivity, $ε=ε_0ε_r$
$∴v=\frac{1}{\sqrt{μ_0μ_rε_0ε_r}}$ ...(1)
By rearrange equation (1), we get
$ε_r=\frac{1}{μ_r}.(\frac{c}{v})^2$
where,
$c=3×10^8m/s$ (speed of light)
$v$, speed of light in the medium = $1.5×10^8m/s$
$μ_r$, Permeability = 0.4
$ε_r=\frac{1}{0.4}.(2)^2$
$=10$