Electric and magnetic fields are intimately connected and together form what is known as the electromagnetic field. The relationship between electric and magnetic fields is described by Maxwell's equations, a set of fundamental equations in electromagnetism.
One of Maxwell's equations, known as Faraday's law of electromagnetic induction, states that a changing magnetic field induces an electric field. Similarly, another equation, called Ampere's law with Maxwell's addition, states that a changing electric field induces a magnetic field. These equations indicate that changes in one field give rise to the other field.
When an electric field changes, it generates a magnetic field that is perpendicular to it. Conversely, when a magnetic field changes, it generates an electric field perpendicular to it. This behavior is due to the mathematical relationship between the two fields in Maxwell's equations.
Additionally, the propagation of electromagnetic waves, such as light, is governed by the principles of electromagnetism. Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and also perpendicular to the direction of wave propagation. This is known as the transverse nature of electromagnetic waves.
The reason for the perpendicularity lies in the nature of the wave equations that govern electromagnetic waves. The wave equations describe how the electric and magnetic fields evolve over space and time. When these equations are solved, the solutions yield waveforms that exhibit the perpendicular relationship between electric and magnetic fields.
In summary, the perpendicularity of electric and magnetic fields arises from the fundamental principles of electromagnetism described by Maxwell's equations and is a consequence of the interplay between electric and magnetic fields as well as the wave nature of electromagnetic waves.