Question:
An EM wave has angular frequency \( \omega \).
Propagation constant \( \mathbf{k} \) and electric field vector \( \mathbf{E} \) is given, then \( \mathbf{B} \) can be represented by:
An EM wave has angular frequency \( \omega \).
Propagation constant \( \mathbf{k} \) and electric field vector \( \mathbf{E} \) is given, then \( \mathbf{B} \) can be represented by:
Propagation constant \( \mathbf{k} \) and electric field vector \( \mathbf{E} \) is given, then \( \mathbf{B} \) can be represented by:
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In an EM wave, the electric field \( \mathbf{E} \), magnetic field \( \mathbf{B} \), and wave vector \( \mathbf{K} \) are all perpendicular to each other, and their relationship is given by the cross product.
Updated On: Apr 7, 2026
- \( \mathbf{B} = \omega (\mathbf{K} \times \mathbf{E}) \)
- \( \mathbf{B} = \omega (\mathbf{E} \times \mathbf{K}) \)
- \( \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \)
- \( \mathbf{B} = \frac{1}{\omega} (\mathbf{E} \times \mathbf{K}) \)
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The Correct Option is C
Solution and Explanation
For an electromagnetic wave, the magnetic field \( \mathbf{B} \), electric field \( \mathbf{E} \), and wave vector \( \mathbf{k} \) are mutually perpendicular and related by the following expression:
\[ \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \] Where: - \( \mathbf{B} \) is the magnetic field vector, - \( \mathbf{K} \) is the propagation constant (wave vector), - \( \mathbf{E} \) is the electric field vector, - \( \omega \) is the angular frequency. Step 1: The relation between the vectors.
In an electromagnetic wave, the magnetic field \( \mathbf{B} \) is perpendicular to both the wave vector \( \mathbf{K} \) and the electric field \( \mathbf{E} \), and the magnitude of \( \mathbf{B} \) is given by:
\[ \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \] This matches with option (C). Therefore, the correct answer is \( \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \). Final Answer: (C) \( \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \)
\[ \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \] Where: - \( \mathbf{B} \) is the magnetic field vector, - \( \mathbf{K} \) is the propagation constant (wave vector), - \( \mathbf{E} \) is the electric field vector, - \( \omega \) is the angular frequency. Step 1: The relation between the vectors.
In an electromagnetic wave, the magnetic field \( \mathbf{B} \) is perpendicular to both the wave vector \( \mathbf{K} \) and the electric field \( \mathbf{E} \), and the magnitude of \( \mathbf{B} \) is given by:
\[ \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \] This matches with option (C). Therefore, the correct answer is \( \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \). Final Answer: (C) \( \mathbf{B} = \frac{1}{\omega} (\mathbf{K} \times \mathbf{E}) \)
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