Yes, the electric and magnetic fields of an electromagnetic wave are in phase and perpendicular to each other. This means that they both reach their maximum and minimum values at the same time, and they are always oriented at 90 degrees to each other.
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electric and magnetic fields of an electromagnetic wave
The direction of the electric and magnetic fields in an electromagnetic wave is determined by the direction of propagation of the wave. The electric field points in the direction of the cross product of the magnetic field and the direction of propagation. The magnetic field points in the direction of the cross product of the electric field and the direction of propagation.
In other words, the electric and magnetic fields of an electromagnetic wave are always aligned in a right-handed triple with the direction of propagation. This means that if you point your thumb in the direction of propagation, your fingers will curl around in the direction of the electric field, and your palm will face in the direction of the magnetic field.