For an electromagnetic wave, the direction of wave propagation k^ is along the direction of E×B.
Since E, B, and k form a mutually perpendicular right-handed system, the direction of the magnetic field is given by B^=k^×E^.
The magnitudes of the electric and magnetic fields are related by B=cE.
Using the relation for the speed of light c=kω, we get B=ωkE.
Combining the magnitude and direction gives:
B=BB^=ωkE(k^×E^)
Since k=kk^ and E=EE^, this simplifies to:
B=ωk×E
Answer: ωk×E