The electric field associated with an e.m. wa | vedclass

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(C) The standard equation for a plane electromagnetic wave is $\vec E = E_0 \cos(kz - \omega t)$.Comparing this with the given equation $\vec E = \hat

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$2$

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(C) The standard equation for a plane electromagnetic wave is $\vec E = E_0 \cos(kz - \omega t)$.Comparing this with the given equation $\vec E = \hat i\,40\, \cos(kz - 6 	imes 10^8 t)$,we identify the angular frequency $\omega = 6 	imes 10^8 \, rad/s$.In a vacuum,the speed of light $c$ is related to the angular frequency $\omega$ and wave vector $k$ by the relation $c = \frac{\omega}{k}$.Given $c = 3 	imes 10^8 \, m/s$,we can solve for $k$:$k = \frac{\omega}{c} = \frac{6 	imes 10^8}{3 	imes 10^8} = 2 \, m^{-1}$.Thus,the value of the wave vector $k$ is $2 \, m^{-1}$.

The electric field associated with an $e.m.$ wave in vacuum is given by $\vec E = \hat i\,40\,\cos \left( {kz - 6 \times {{10}^8}\,t} \right)$,where $E$,$z$,and $t$ are in $V/m$,$m$,and $s$ respectively. The value of the wave vector $k$ is ....... $m^{-1}$.

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