The relationship between the electric and magnetic fields in an electromagnetic wave and the direction of wave propagation is governed by Maxwell's equations, which describe the behavior of electromagnetic fields. These equations, along with experimental observations, provide evidence that the electric and magnetic fields are perpendicular to the direction of wave propagation.
One way to demonstrate this relationship is through the wave equation derived from Maxwell's equations. In a simplified form, the wave equation for an electromagnetic wave propagating in a vacuum can be written as:
∇²E = (1/c²) ∂²E/∂t²
∇²B = (1/c²) ∂²B/∂t²
where E represents the electric field, B represents the magnetic field, c is the speed of light, ∇² is the Laplacian operator, and ∂/∂t represents the partial derivative with respect to time.
Solutions to the wave equation reveal that the electric and magnetic fields in an electromagnetic wave are perpendicular to each other and to the direction of wave propagation. The fields are orthogonal, meaning they form a right angle with each other.
Experimental observations also support this perpendicular relationship. For example, the phenomenon of polarization demonstrates that electromagnetic waves can be filtered or manipulated based on the orientation of their electric field vectors. Polarization filters can block waves with electric field components oriented in a specific direction while allowing waves with perpendicular components to pass through. This behavior is consistent with the understanding that the electric and magnetic fields are perpendicular to each other.
Additionally, experiments such as the Faraday effect and the Hall effect show the interaction between electric and magnetic fields in a way that aligns with the perpendicular relationship.
In summary, the perpendicular relationship between the electric and magnetic fields in electromagnetic waves is supported by theoretical derivations from Maxwell's equations and confirmed through experimental observations and phenomena related to polarization and electromagnetic interactions.