The oscillating magnetic field in a plane ele | vedclass

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Question

(A) The given equation for the magnetic field is $B_{y} = B_{0} \sin(kx - \omega t)$.Comparing this with the given equation $B_{y} = 5 	imes 10^{-6}

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$15 	imes 10^{2} 	ext{ Vm}^{-1}$

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(A) The given equation for the magnetic field is $B_{y} = B_{0} \sin(kx - \omega t)$.Comparing this with the given equation $B_{y} = 5 	imes 10^{-6} \sin(5000\pi x - 4 	imes 10^{11}\pi t)$,we identify the amplitude of the magnetic field as $B_{0} = 5 	imes 10^{-6} 	ext{ T}$.The speed of the electromagnetic wave $c$ is related to the electric field amplitude $E_{0}$ and magnetic field amplitude $B_{0}$ by the relation $E_{0} = c B_{0}$.Using the speed of light $c = 3 	imes 10^{8} 	ext{ m/s}$,we calculate:$E_{0} = (3 	imes 10^{8} 	ext{ m/s}) 	imes (5 	imes 10^{-6} 	ext{ T})$$E_{0} = 15 	imes 10^{2} 	ext{ V/m} = 1500 	ext{ V/m}$.

The oscillating magnetic field in a plane electromagnetic wave is given by $B_{y} = 5 \times 10^{-6} \sin(1000\pi(5x - 4 \times 10^{8}t)) \text{ T}$. The amplitude of the electric field will be:

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