What is the relative permittivity of a medium of relative permeability 1.0 in which an electromagnetic wave travels at a speed of $2×10^8 ms^{-1}$?

2.25

The correct answer is Option (3) → 2.25

The speed of the electromagnetic wave in a medium is related to the relative permittivity ($ε_r$) and Relative permeability ($μ_r$),

$v=\frac{c}{\sqrt{ε_rμ_r}}$

$⇒ε_r=\frac{c^2}{v^2μ_r}=\left(\frac{3×10^8}{2×10^8}\right)^2$

$ε_r=\left(\frac{3}{2}\right)^2=\frac{9}{4}=2.25$