Final answer:
In electromagnetic waves, the electric and magnetic fields are in phase and perpendicular to each other and the direction of wave propagation due to the nature of mutual induction and Maxwell's equations.
Step-by-step explanation:
In an electromagnetic wave, the electric field (E) and the magnetic field (M or B) are always in phase and perpendicular to each other, as well as to the direction of propagation. This configuration arises from the nature of how electromagnetic waves are produced and propagate through space. An oscillating electric field generates a magnetic field, and in turn, this oscillating magnetic field generates an electric field. This interdependence is described as mutual induction, a principle central to Maxwell's equations, which govern the behavior of electromagnetic waves.
The in-phase relationship between the electric and magnetic fields is necessary for the energy in the wave to propagate through space effectively. If these fields were out of phase, it would imply energy being absorbed back into the source rather than radiating away, something that does not occur in free space propagation. The perpendicular orientation of the two fields ensures that the wave is transverse, with the force exerted by the combined fields acting in the direction of propagation, thus enabling the transfer of energy and momentum.