Electric and magnetic fields are intimately connected and are two aspects of the same fundamental force, known as the electromagnetic force. The relationship between electric and magnetic fields is described by Maxwell's equations, a set of fundamental equations that govern the behavior of electromagnetic fields.
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 or a current induces a magnetic field.
When an electric field changes in time, it creates a magnetic field that circulates around it. Conversely, when a magnetic field changes in time, it induces an electric field that forms closed loops around it. These two phenomena are interrelated and give rise to electromagnetic waves.
In an electromagnetic wave, such as light or radio waves, the electric and magnetic fields oscillate perpendicular to each other and also perpendicular to the direction of wave propagation. This perpendicular relationship arises from the mathematical relationships and properties of the electromagnetic waves described by Maxwell's equations.
The perpendicular nature of electric and magnetic fields in an electromagnetic wave is a consequence of the underlying symmetry and self-propagation of the fields. It is a fundamental property of electromagnetic waves and is consistent with experimental observations and theoretical predictions.