Question

An electromagnetic wave in vacuum has the electric and magnetic fields E and B, which are always perpendicular to each other. The direction of polarization is given by X and that of wave propagation by k. Then :
(1) X || B and k || BxE




(2) X || E and k || ExB






(3) X || B and k || ExB






(4) X || E and k || BxE

I need to know the logic also.

Answer 1

In a polarized wave, the fields point in certain directions. The direction of polarization means the direction in which the Electric field vector points.
so, X would be parallel to E
the direction of propogation would be perpendicular to the directions of electric and magnetic field. An Electromagnetic wave is a transverse wave. This means wave motions is in a direction perpendicular to oscillations.
Hence k would be perpendicular to both B & E.
Thus k || E x B
We have chosen a convention such that E x B gives the forward direction of the wave.

Answer 2

Thnxx @zaphodplaysitsafe

Answer 3

you're welcome @lordcyborg