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
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
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Remember that both permeability and permittivity affect how electromagnetic waves propagate through a medium.
Updated On: Mar 19, 2025
- \(3 \times 10^8 \, {m/s}\)
- \(\sqrt{3} \times 10^8 \, {m/s}\)
- \(2.2 \times 10^8 \, {m/s}\)
- \(\sqrt{2} \times 10^8 \, {m/s}\)
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The Correct Option is B
Solution and Explanation
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), \( \sqrt{3} \times 10^8 \, \text{m/s} \).
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