The magnetic field in a plane electromagnetic | vedclass

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Question

(B) Given,magnetic field in a plane electromagnetic wave is $B = (3 	imes 10^{-7} 	ext{ T}) \sin (3 	imes 10^4 x + 9 	imes 10^{12} t) \hat{j}$.Her

Vedclass · Accepted Answer

$90 \sin (3 	imes 10^4 x + 9 	imes 10^{12} t) \hat{k} 	ext{ Vm}^{-1}$

Vedclass · Answer

(B) Given,magnetic field in a plane electromagnetic wave is $B = (3 	imes 10^{-7} 	ext{ T}) \sin (3 	imes 10^4 x + 9 	imes 10^{12} t) \hat{j}$.Here,the amplitude of the magnetic field is $B_0 = 3 	imes 10^{-7} 	ext{ T}$.The amplitude of the electric field $E_0$ is given by $E_0 = B_0 c$,where $c = 3 	imes 10^8 	ext{ m/s}$ is the speed of light.$E_0 = (3 	imes 10^{-7}) 	imes (3 	imes 10^8) = 90 	ext{ V/m}$.The wave propagates in the negative $x$-direction (indicated by the $+kx$ term in the phase).The direction of propagation is given by the direction of $\vec{E} 	imes \vec{B}$.Since the wave travels in the $-\hat{i}$ direction and $\vec{B}$ is in the $\hat{j}$ direction,we have $\hat{n}_E 	imes \hat{j} = -\hat{i}$.This implies $\hat{n}_E = \hat{k}$.Therefore,the electric field is $E = E_0 \sin (kx + \omega t) \hat{k} = 90 \sin (3 	imes 10^4 x + 9 	imes 10^{12} t) \hat{k} 	ext{ Vm}^{-1}$.

The magnetic field in a plane electromagnetic wave is given as $B = (3 \times 10^{-7} \text{ T}) \sin (3 \times 10^4 x + 9 \times 10^{12} t) \hat{j}$. The electric field of this wave is given as:

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