The electric field of a plane electromagnetic | vedclass

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(B) For an electromagnetic wave, the direction of propagation is given by the vector $\vec{k}_{dir} = \hat{k}$ (since the phase is $kz - \omega t$).Th

Vedclass · Accepted Answer

$-\hat{i} + \hat{j}$

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(B) For an electromagnetic wave, the direction of propagation is given by the vector $\vec{k}_{dir} = \hat{k}$ (since the phase is $kz - \omega t$).The electric field vector is $\vec{E} = E_0(\hat{i} + \hat{j})$.The magnetic field $\vec{B}$ is perpendicular to both the direction of propagation and the electric field $\vec{E}$.The direction of $\vec{B}$ is given by the cross product $\vec{k}_{dir} 	imes \vec{E}$.$\vec{B}_{dir} = \hat{k} 	imes (\hat{i} + \hat{j}) = (\hat{k} 	imes \hat{i}) + (\hat{k} 	imes \hat{j}) = \hat{j} - \hat{i} = -\hat{i} + \hat{j}$.Thus, the direction of the magnetic field is $-\hat{i} + \hat{j}$.

The electric field of a plane electromagnetic wave of wave number $k$ and angular frequency $\omega$ is given by $\vec{E} = E_0(\hat{i} + \hat{j}) \sin(kz - \omega t)$. Which of the following gives the direction of the associated magnetic field $\vec{B}$?

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