Question

Wave propagates whose electric field is given by \( \mathbf{E} = 69 \sin(\omega t - kx) \hat{j \). Find the direction of magnetic field.}

• A. \( \hat{k} \)
• B. \( -\hat{k} \)
• C. \( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \)
• D. \( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \)

Hint:

In electromagnetic waves, the electric and magnetic fields are always perpendicular to each other and to the direction of wave propagation.

Answer 1

The Correct Option is A

Step 1: Use the relation \( \mathbf{E} \times \mathbf{B} = \mathbf{C} \).
For an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of propagation. Since \( \mathbf{E} \) is along the \( \hat{j} \) direction, the magnetic field will be along the \( \hat{k} \) direction.
Step 2: Conclusion.
The direction of the magnetic field is along \( \hat{k} \), which corresponds to option (1).