A plane electromagnetic wave of frequency 20, | vedclass

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(B) Given: $\overrightarrow{E} = 6.6 \hat{j} \, V/m$, frequency $f = 20 \, MHz$, and the wave propagates along the $x$-direction $(\hat{i})$.The magni

Vedclass · Accepted Answer

$2.2 	imes 10^{-8} \hat{k} \, T$

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(B) Given: $\overrightarrow{E} = 6.6 \hat{j} \, V/m$, frequency $f = 20 \, MHz$, and the wave propagates along the $x$-direction $(\hat{i})$.The magnitude of the magnetic field is given by $B = \frac{E}{c}$, where $c = 3 	imes 10^8 \, m/s$ is the speed of light.$B = \frac{6.6}{3 	imes 10^8} = 2.2 	imes 10^{-8} \, T$.The direction of the magnetic field is determined by the relation $\hat{k} = \hat{E} 	imes \hat{B}$, where $\hat{k}$ is the direction of wave propagation.Here, $\hat{i} = \hat{j} 	imes \hat{B}$.Since $\hat{j} 	imes \hat{k} = \hat{i}$, the direction of $\overrightarrow{B}$ must be $\hat{k}$.Therefore, $\overrightarrow{B} = 2.2 	imes 10^{-8} \hat{k} \, T$.

$A$ plane electromagnetic wave of frequency $20\, MHz$ propagates in free space along the $x$-direction. At a particular space and time, $\overrightarrow{E} = 6.6 \hat{j} \, V/m$. What is $\overrightarrow{B}$ at this point?

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