The electric field associated with an electro | vedclass

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(A) The standard equation for an electromagnetic wave traveling in the $z$-direction is given by $\vec{E} = E_{0} \cos (kz - \omega t) \hat{i}$.Compar

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$2$

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(A) The standard equation for an electromagnetic wave traveling in the $z$-direction is given by $\vec{E} = E_{0} \cos (kz - \omega t) \hat{i}$.Comparing the given equation $\vec{E} = \hat{i} 40 \cos (kz - 6 	imes 10^{8} t)$ with the standard form,we identify the angular frequency $\omega = 6 	imes 10^{8} \, rad/s$.In vacuum,the relationship between the wave vector $k$,angular frequency $\omega$,and the speed of light $c$ is given by $k = \frac{\omega}{c}$.Given $c = 3 	imes 10^{8} \, m/s$,we calculate $k = \frac{6 	imes 10^{8}}{3 	imes 10^{8}} = 2 \, m^{-1}$.

The electric field associated with an electromagnetic $(EM)$ wave in vacuum is given by $\vec{E} = \hat{i} 40 \cos (kz - 6 \times 10^{8} t)$,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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