Question
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
A.
$$\overrightarrow E = - {E_0}\cos \left( {\omega t + \frac{{2\pi }}{\lambda }y} \right)\hat x$$
B.
$$\overrightarrow E = {E_0}\cos \left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat x$$
C.
$$\overrightarrow E = {E_0}\cos \left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat z$$
D.
$$\overrightarrow E = - {E_0}\cos \left( {\omega t + \frac{{2\pi }}{\lambda }y} \right)\hat z$$
Answer :
$$\overrightarrow E = {E_0}\cos \left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat z$$
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
$$\vec E = {E_0}\cos \left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat z$$