In a simple, charge-free medium, what is the relationship between the electric field E , magnetic field H , and wave vector k of a time-harmonic plane wave?

Correct option is C

In a simple, linear, homogeneous, isotropic, and charge-free medium, a time-harmonic plane electromagnetic wave has the following fundamental properties:

• The wave vector k indicates the direction of propagation.
• The electric field E and magnetic field H are both transverse to the direction of propagation.
• Hence, E is perpendicular to k and H is perpendicular to k.
• Additionally, E, H, and k are mutually perpendicular, with E × H pointing in the direction of k (right-hand rule).

Therefore, the correct relationship is that both E and H are perpendicular to k.