An electromagnetic wave travels in free space | vedclass

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Question

(B) The relationship between the electric field $\vec{E}$ and the magnetic field $\vec{B}$ in an electromagnetic wave is given by $\vec{E} = c(\vec{B}

Vedclass · Accepted Answer

$-60$

Vedclass · Answer

(B) The relationship between the electric field $\vec{E}$ and the magnetic field $\vec{B}$ in an electromagnetic wave is given by $\vec{E} = c(\vec{B} 	imes \hat{n})$, where $\hat{n}$ is the unit vector in the direction of wave propagation.Here, the wave propagates along the $x$-direction, so $\hat{n} = \hat{i}$.The speed of light in free space is $c = 3 	imes 10^8 	ext{ m/s}$.Given $\vec{B} = 2 	imes 10^{-7} \hat{j} 	ext{ T}$.Substituting these values: $\vec{E} = (3 	imes 10^8 	ext{ m/s}) 	imes (2 	imes 10^{-7} \hat{j} 	ext{ T} 	imes \hat{i})$.Since $\hat{j} 	imes \hat{i} = -\hat{k}$, we have $\vec{E} = (3 	imes 10^8) 	imes (2 	imes 10^{-7}) 	imes (-\hat{k}) = 60 	imes (-\hat{k}) = -60\hat{k} 	ext{ V/m}$.

An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec{B} = 2 \times 10^{-7} \hat{j} \text{ T}$ is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is . . . . . . $V$/m. (in $\hat{k}$)

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