In an electromagnetic wave, the magnitudes of the electric field (E) and magnetic field (B) are related to each other by a fundamental property of electromagnetic waves called the wave impedance (Z).
The wave impedance (Z) is defined as the ratio of the magnitude of the electric field (E) to the magnitude of the magnetic field (B) in an electromagnetic wave. Mathematically, it can be expressed as:
Z = E / B
The wave impedance is a constant value in a given medium and is determined by the properties of that medium. In a vacuum or free space, the wave impedance is equal to the impedance of free space, which is approximately 376.73 ohms.
The relationship between the magnitudes of E and B can be understood as follows: when an electromagnetic wave propagates through a medium, the electric field and the magnetic field are orthogonal to each other and oscillate in a coordinated manner. The ratio of their magnitudes, given by the wave impedance, remains constant as the wave travels.
It's important to note that the electric and magnetic fields in an electromagnetic wave are not independent of each other but are tightly coupled and mutually sustaining. Changes in one field induce changes in the other, creating a self-propagating wave.