Question

Electromagnetic waves travel in a medium with a speed of \( 1.5 \times 10^8 \, \text{ms}^{-1} \). The relative permeability of the medium is \( 2.0 \). The relative permittivity will be:

• A. 5
• B. 4
• C. 1
• D. 2

Answer 1

The Correct Option is D

The speed of electromagnetic waves in a medium is related to its relative permeability (\( \mu_r \)) and relative permittivity (\( \varepsilon_r \)) by the equation:

\[ \varepsilon_r \mu_r = \frac{c^2}{v^2}, \]

where:
- \( c = 3 \times 10^8 \, \text{ms}^{-1} \) (speed of light in vacuum),
- \( v = 1.5 \times 10^8 \, \text{ms}^{-1} \) (speed of light in the medium),
- \( \mu_r = 2.0 \) (relative permeability of the medium).

Substituting the given values:

\[ \varepsilon_r \times 2 = \frac{(3 \times 10^8)^2}{(1.5 \times 10^8)^2}. \]

Simplify:

\[ \varepsilon_r \times 2 = \frac{9 \times 10^{16}}{2.25 \times 10^{16}}. \]

\[ \varepsilon_r \times 2 = 4. \]

\[ \varepsilon_r = 2. \]

Final Answer: \( \varepsilon_r = 2 \) (Option 4)