Question

An electromagnetic wave travels in a medium of relative permeability \(1.3\) and relative permittivity \(2.3\). Then the speed of an electromagnetic wave in that medium is

• A. \(3 \times 10^8 \, {m/s}\)
• B. \(\sqrt{3} \times 10^8 \, {m/s}\)
• C. \(2.2 \times 10^8 \, {m/s}\)
• D. \(\sqrt{2} \times 10^8 \, {m/s}\)

Hint:

Remember that both permeability and permittivity affect how electromagnetic waves propagate through a medium.

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:

• \( v \) is the speed of the electromagnetic wave in the medium,
• \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light in vacuum,
• \( \mu_r \) is the relative permeability of the medium,
• \( \epsilon_r \) is the relative permittivity of the medium.

Substituting the given values:

\[ v = \frac{3 \times 10^8}{\sqrt{1.3 \times 2.3}} \]

First, calculate \( 1.3 \times 2.3 = 2.99 \), and then:

\[ v = \frac{3 \times 10^8}{\sqrt{2.99}} = \frac{3 \times 10^8}{\sqrt{3}} = \sqrt{3} \times 10^8 \, \text{m/s} \]

Thus, the correct answer is Option (2), \( \sqrt{3} \times 10^8 \, \text{m/s} \).