The electric field in a plane electromagnetic | vedclass

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(C) The general equation for a plane electromagnetic wave is $E = E_0 \sin(kx - \omega t)$.Comparing this with the given equation $E = 50 \sin(500x -

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$\frac{2}{3} C$

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(C) The general equation for a plane electromagnetic wave is $E = E_0 \sin(kx - \omega t)$.Comparing this with the given equation $E = 50 \sin(500x - 10 	imes 10^{10}t)$,we get:Wave number $k = 500 \, 	ext{rad/m}$Angular frequency $\omega = 10 	imes 10^{10} \, 	ext{rad/s}$The velocity of the wave $v$ is given by $v = \frac{\omega}{k}$.Substituting the values: $v = \frac{10 	imes 10^{10}}{500} = \frac{10^{11}}{5 	imes 10^2} = 2 	imes 10^8 \, 	ext{m/s}$.Since the speed of light in vacuum is $C = 3 	imes 10^8 \, 	ext{m/s}$,we can write $v = \frac{2}{3} 	imes 3 	imes 10^8 = \frac{2}{3} C$.

The electric field in a plane electromagnetic wave is given by $E = 50 \sin(500x - 10 \times 10^{10}t) \, V/m$. The velocity of the electromagnetic wave in this medium is: (Given $C = \text{speed of light in vacuum}$)

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