$(10$ marks$)$ Consider a electromagnetic plane wave propagating along direction in vacuum, therefore both electric field and magnetic field are functions onlyof and tme $($i$.$e$.,).$ Show t the electromagnetic wave in vacuum is transverse $($i$.$e$.$ there is no oscillation of electromagnetic fiel along the propagating direction$).(10$ marks$)$ Considering special case that a polarized electromagnetic wave with the time varying electric field parallel to direction propagating along direction in vacuum $($i$.$e$.),$ sho that the time$-$varying magnetic field can only have component