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Question

(B) For an electromagnetic wave, the relationship between the electric field $\vec{E}$, the magnetic field $\vec{B}$, and the propagation vector $\vec

Vedclass · Accepted Answer

$\frac{\vec{k} 	imes \vec{E}}{\omega}$

Vedclass · Answer

(B) For an electromagnetic wave, the relationship between the electric field $\vec{E}$, the magnetic field $\vec{B}$, and the propagation vector $\vec{k}$ is given by the Maxwell-Faraday equation.According to Faraday's law in differential form, $
abla 	imes \vec{E} = -\frac{\partial \vec{B}}{\partial t}$.For a plane electromagnetic wave, $\vec{E} = \vec{E}_0 \cos(\vec{k} \cdot \vec{r} - \omega t)$ and $\vec{B} = \vec{B}_0 \cos(\vec{k} \cdot \vec{r} - \omega t)$.Substituting these into the differential equation, we get $\vec{k} 	imes \vec{E} = \omega \vec{B}$.Therefore, the magnetic field is given by $\vec{B} = \frac{\vec{k} 	imes \vec{E}}{\omega}$.

For an electromagnetic wave propagating through vacuum, $\vec{k}$, $\vec{E}$, and $\omega$ represent the propagation vector, electric field, and angular frequency, respectively. The magnetic field associated with this wave is represented by:

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