Electric and Magnetic Field Directions in EM Wave – Rankers Physics

Properties of EM Waves: Practice Problem & Solution

For a plane EM wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (\(\vec{E}\) ) and magnetic field (\(\vec{B}\) ) respectively?
\(-\hat{j} + \hat{k}, -\hat{j} + \hat{k}\)
\(\hat{j} + \hat{k}, \hat{j} + \hat{k}\)
\(-\hat{j} + \hat{k}, -\hat{j} - \hat{k}\)
\(\hat{j} + \hat{k}, -\hat{j} - \hat{k}\)

Solution Explained:

To solve this problem, we apply the core principles of Properties of EM Waves. Understanding the underlying formula is key to arriving at the correct answer below:

The direction of propagation of an electromagnetic wave is along \(\vec{E} \times \vec{B}\). Here, \((-\hat{j} + \hat{k}) \times (-\hat{j} - \hat{k}) = 2\hat{i}\), which points in the positive x-direction.

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