A plane electromagnetic wave of frequency 25 | vedclass

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Question

(A) For an electromagnetic wave traveling in free space, the relationship between the electric field $\vec{E}$ and the magnetic field $\vec{B}$ is giv

Vedclass · Accepted Answer

$2.1 	imes 10^{-8} \hat{k} 	ext{ T}$

Vedclass · Answer

(A) For an electromagnetic wave traveling in free space, the relationship between the electric field $\vec{E}$ and the magnetic field $\vec{B}$ is given by $B = \frac{E}{c}$, where $c$ is the speed of light in vacuum $(c \approx 3 	imes 10^8 	ext{ m/s})$.Given $E = 6.3 	ext{ V/m}$, the magnitude of the magnetic field is $B = \frac{6.3}{3 	imes 10^8} = 2.1 	imes 10^{-8} 	ext{ T}$.The direction of propagation is along the $X$-direction $(\hat{i})$, and the electric field is along the $Y$-direction $(\hat{j})$.Since the wave propagates in the direction of $\vec{E} 	imes \vec{B}$, we have $\hat{i} = \hat{j} 	imes \hat{B}$.This implies $\hat{B} = \hat{k}$.Therefore, the magnetic field is $\vec{B} = 2.1 	imes 10^{-8} \hat{k} 	ext{ T}$.

$A$ plane electromagnetic wave of frequency $25 \text{ MHz}$ travels in free space along the $X$-direction. At a particular point in space and time, the electric field is $\vec{E} = 6.3 \hat{j} \text{ V m}^{-1}$. What is the magnetic field $\vec{B}$ at that point?

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