1. The problem statement, all variables and given/known data which of the following proposed space-time dependent electric fields in vacuum is/are allowed by the equations of EM theory? a) $$E_x=E_1\sin(kz-wt),E_y=E_2\sin(kz-wt),E_z=0$$ b) $$E_x=E_1\sin(kz-wt),E_y=2E_1\cos(kz-wt),E_z=0$$ c) $$E_x=E_1\sin(kz-wt),E_y=0,E_z=E_2\sin(kz-wt)$$ 2. Relevant equations $$E = E_0\sin(kz-wt)$$ 3. The attempt at a solution I think all the three equations are allowed according to the normal waveform. However I do not know what exactly to look for in such case that does not make it an allowed waveform. I would appreciate if someone could show an example that is not a waveform if my answer turns out to be correct.