Question

An electromagnetic wave travels in a medium with a speed of \( 2 \times 10^8 \, \text{ms}^{-1} \). The relative permeability of the medium is 1. Then the relative permittivity is.

• A. 1.75
• B. 2
• C. 2.25
• D. 2.75

Hint:

To find the relative permittivity of a medium, use the relationship between the speed of light in the medium and the speed of light in vacuum.

Answer 1

The Correct Option is C

The speed of light in a medium is given by: \[ v = \frac{c}{\sqrt{\mu_r \epsilon_r}} \] Where: - \( v \) is the speed of the electromagnetic wave in the medium - \( c \) is the speed of light in a vacuum - \( \mu_r \) is the relative permeability of the medium - \( \epsilon_r \) is the relative permittivity of the medium Given that \( \mu_r = 1 \) and \( v = 2 \times 10^8 \, \text{ms}^{-1} \), and \( c = 3 \times 10^8 \, \text{ms}^{-1} \), we can solve for \( \epsilon_r \): \[ \epsilon_r = \frac{c^2}{v^2} = \frac{(3 \times 10^8)^2}{(2 \times 10^8)^2} = 2.25 \] Thus, the relative permittivity is \( 2.25 \).