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An electromagnetic wave with frequency $\omega $ and wavelength $\lambda $ travels in the $+ y$ direction . Its magnetic field is along $+\, x-$ axis. The vector equation for the associated electric field ( of amplitude $E_0$) is
$\vec E = - {E_0}\,\cos \,\left( {\omega t + \frac{{2\pi }}{\lambda }y} \right)\hat x$
$\vec E = {E_0}\,\cos \,\left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat x$
$\vec E = {E_0}\,\cos \,\left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat z$
$\vec E = - {E_0}\,\cos \,\left( {\omega t + \frac{{2\pi }}{\lambda }y} \right)\hat z$
Solution
In an electromagnetic wave electric field and magnetic field are perpendicular to the direction of propagation of wave. The vector equation for the electric field is
$\vec E = {E_0}\,\cos \,\left( {\omega t – \frac{{2\pi }}{\lambda }y} \right)\hat z$
