An electromagnetic wave travels in a medium at a speed of $2×10^8 m/s$. If the relative permeability ($μ_r$) of the medium is 1.0, then the relative permittivity ($ε_r$) of the medium is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.25
Speed of wave in medium: $v = \frac{c}{\sqrt{\mu_r \varepsilon_r}}$
Given: $v = 2 \times 10^8 \ \text{m/s}, \ c = 3 \times 10^8 \ \text{m/s}, \ \mu_r = 1$
$2 \times 10^8 = \frac{3 \times 10^8}{\sqrt{\varepsilon_r}}$
$\sqrt{\varepsilon_r} = \frac{3 \times 10^8}{2 \times 10^8} = \frac{3}{2}$
$\varepsilon_r = \left(\frac{3}{2}\right)^2 = \frac{9}{4} = 2.25$
∴ Relative permittivity $\varepsilon_r = 2.25$