Question:
If the average power per unit area delivered by an electromagnetic wave is
\[
9240\ \text{W m}^{-2}
\]
then the amplitude of the oscillating magnetic field in the EM wave is
If the average power per unit area delivered by an electromagnetic wave is
\[ 9240\ \text{W m}^{-2} \] then the amplitude of the oscillating magnetic field in the EM wave is
\[ 9240\ \text{W m}^{-2} \] then the amplitude of the oscillating magnetic field in the EM wave is
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For electromagnetic waves, intensity is related to magnetic field amplitude by \(I=\dfrac{cB_0^2}{2\mu_0}\).
Updated On: Jun 15, 2026
- \(4.4\ \mu\text{T}\)
- \(6.6\ \mu\text{T}\)
- \(8.8\ \mu\text{T}\)
- \(10.2\ \mu\text{T}\)
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The Correct Option is C
Solution and Explanation
Step 1: Use the relation between intensity and magnetic field amplitude.
The average intensity of an electromagnetic wave is given by
\[ I=\frac{cB_0^2}{2\mu_0} \]
where
\[ I=9240\ \text{W m}^{-2} \] is the intensity,
\[ c=3\times10^8\ \text{m s}^{-1} \] is the speed of light, and
\[ \mu_0=4\pi\times10^{-7}\ \text{H m}^{-1} \] is the permeability of free space.
Step 2: Rearrange the formula for \(B_0\).
\[ B_0=\sqrt{\frac{2\mu_0 I}{c}} \]
Substituting the values,
\[ B_0=\sqrt{ \frac{2(4\pi\times10^{-7})(9240)} {3\times10^8} } \]
Step 3: Simplify the expression.
\[ B_0=\sqrt{ \frac{8\pi\times9240\times10^{-7}} {3\times10^8} } \]
Using \(\pi\approx3.14\),
\[ B_0\approx\sqrt{7.74\times10^{-11}} \]
\[ B_0\approx8.8\times10^{-6}\ \text{T} \]
\[ B_0=8.8\ \mu\text{T} \]
Step 4: Final conclusion.
Hence, the amplitude of the oscillating magnetic field is
\[ \boxed{8.8\ \mu\text{T}} \]
The average intensity of an electromagnetic wave is given by
\[ I=\frac{cB_0^2}{2\mu_0} \]
where
\[ I=9240\ \text{W m}^{-2} \] is the intensity,
\[ c=3\times10^8\ \text{m s}^{-1} \] is the speed of light, and
\[ \mu_0=4\pi\times10^{-7}\ \text{H m}^{-1} \] is the permeability of free space.
Step 2: Rearrange the formula for \(B_0\).
\[ B_0=\sqrt{\frac{2\mu_0 I}{c}} \]
Substituting the values,
\[ B_0=\sqrt{ \frac{2(4\pi\times10^{-7})(9240)} {3\times10^8} } \]
Step 3: Simplify the expression.
\[ B_0=\sqrt{ \frac{8\pi\times9240\times10^{-7}} {3\times10^8} } \]
Using \(\pi\approx3.14\),
\[ B_0\approx\sqrt{7.74\times10^{-11}} \]
\[ B_0\approx8.8\times10^{-6}\ \text{T} \]
\[ B_0=8.8\ \mu\text{T} \]
Step 4: Final conclusion.
Hence, the amplitude of the oscillating magnetic field is
\[ \boxed{8.8\ \mu\text{T}} \]
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