Question

For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively

• A. \(-\hat{j}+\hat{k},-\hat{j}+\hat{k}\)
• B. \(\hat{j}+\hat{k},\hat{j}+\hat{k}\)
• C. \(-\hat{j}+\hat{k},-\hat{j}-\hat{k}\)
• D. \(\hat{j}+\hat{k},-\hat{j}-\hat{k}\)

Answer 1

The Correct Option is C

To solve this problem, we need to understand the properties of electromagnetic waves (EM waves). In a plane electromagnetic wave, the electric field (\( \mathbf{E} \)) and the magnetic field (\( \mathbf{B} \)) are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.

For a plane electromagnetic wave propagating in the \(x\)-direction, the direction of these fields can be determined by the following rules:

• The electric field (\( \mathbf{E} \)) is always perpendicular to the direction of wave propagation.
• The magnetic field (\( \mathbf{B} \)) is also perpendicular to the direction of wave propagation and to the electric field.
• The direction of propagation of the wave is given by the cross product \( \mathbf{E} \times \mathbf{B} \).

Let's consider each option to see which fits these criteria: 

1. \(-\hat{j}+\hat{k},-\hat{j}+\hat{k}\): This option suggests both fields are in the same plane, which would violate the perpendicularity criterion.
2. \(\hat{j}+\hat{k},\hat{j}+\hat{k}\): Again, both fields point in the same general direction, which is not possible because they should be perpendicular to each other.
3. \(-\hat{j}+\hat{k},-\hat{j}-\hat{k}\): In this combination, the electric field could be in the \(-\hat{j}+\hat{k}\) direction, while the magnetic field is in the perpendicular plane, maintaining perpendicularity to the wave direction and to each other.
4. \(\hat{j}+\hat{k},-\hat{j}-\hat{k}\): This setup does suggest different planes, but does not align correctly as the cross product would not give a clear \(+\hat{i}\) direction which is necessary for propagation in the \(x\)-direction.

Therefore, the correct choice is option three, \(-\hat{j}+\hat{k},-\hat{j}-\hat{k}\), where the electric field and magnetic field are correctly oriented such that their cross product results in the propagation along the \(x\)-direction.