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  4. An electromagnetic wave is transposing energy in the negative y-direction. At one point and one instant the magnetic field is in the positive x-direction. The electric field at that point and instant in

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Q. An electromagnetic wave is transposing energy in the negative y-direction. At one point and one instant the magnetic field is in the positive x-direction. The electric field at that point and instant in

Electromagnetic Waves

Solution:

In an electromagnetic wave, the direction of energy flow is along the direction of the wave propagation. Therefore, the wave propagates along negative y-direction. Magnetic field $\left(\overrightarrow{B}\right)$ is along the positive x-direction and the wave propagates along negative y-direction. Therefore, electric field $\left(\overrightarrow{E}\right)$ should be in a direction perpendicular to both x and y-axes. Using vector algebra $\overrightarrow{E}\times\overrightarrow{B}$ should bealong negative y-direction.
Since $\left(-\hat{j}\right)=\left(-\hat{k}\right)\times\left(\hat{i}\right), \overrightarrow{E}$ is along negative z-direction.