Question

Speed of electromagnetic wave in a medium having relative permittivity \( \epsilon_r \) and relative permeability \( \mu_r \) is (speed of light in air, \( c = 3 \times 10^8 \, \text{m/s} \))

• A. \( \frac{1}{\sqrt{\mu_r \epsilon_r}} \)
• B. \( \frac{c}{\sqrt{\mu_r \epsilon_r}} \)
• C. \( c \sqrt{\frac{\mu_r}{\epsilon_r}} \)
• D. \( \frac{c}{\mu_r \epsilon_r} \)

Hint:

The speed of light in a medium depends on both its relative permeability and permittivity. A higher value of either will reduce the speed of the wave.

Answer 1

The Correct Option is B

The speed of an electromagnetic wave in a medium is given by the formula: \[ v = \frac{c}{\sqrt{\mu_r \epsilon_r}} \] where: - \( c \) is the speed of light in a vacuum (or air),
- \( \mu_r \) is the relative permeability of the medium,
- \( \epsilon_r \) is the relative permittivity of the medium.
This equation is derived from the fundamental properties of the electromagnetic wave's propagation in a medium. Therefore, the correct answer is (B).