The electric field of an electromagnetic wave | vedclass

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Question

(B) The electric field is given by $\vec{E} = E_0 \cos(\omega t - kz) \hat{i}$.In an electromagnetic wave, the relationship between the electric field

Vedclass · Accepted Answer

$\vec{B} = \frac{E_0}{C} \cos(\omega t - kz) \hat{j}$

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(B) The electric field is given by $\vec{E} = E_0 \cos(\omega t - kz) \hat{i}$.In an electromagnetic wave, the relationship between the electric field amplitude $E_0$ and the magnetic field amplitude $B_0$ is given by $B_0 = \frac{E_0}{C}$, where $C$ is the speed of light.The direction of propagation of the wave is given by the direction of the vector $\vec{E} 	imes \vec{B}$.Here, the wave propagates in the $+z$ direction $(\hat{k})$.Given $\vec{E}$ is in the $\hat{i}$ direction, we have $\hat{i} 	imes \hat{B} = \hat{k}$.This implies $\hat{B} = \hat{j}$.Thus, the magnetic field vector is $\vec{B} = \frac{E_0}{C} \cos(\omega t - kz) \hat{j}$.

The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_0 \cos(\omega t - kz) \hat{i}$. The corresponding magnetic induction vector will be:

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