Maxwell’s equations led him to realize the existence of self propagating electromagnetic waves. Using Maxwell’s equations we can see that as charges propagate they generate an electromagnetic wave which in turn induces a magnetic wave perpendicular to it.
E = electric field, B = magnetic field d s = element of Amperian loop Φ = flux, t = time μ 0 = permeability of free space ε 0 = permittivity of free space
The amplitude of the magnetic field is related to the amplitude of the electric field: Also, the two fields are everywhere orthogonal:
This is a wave equation, with solution: E = electric field, B = magnetic field E max = amplitude, B max = amplitude k = angular wave number ω = angular frequency x = position, t = time φ = phase constant
This is a wave equation, with solution: The propagation speed
Electromagnetic waves travel more slowly through a medium by a factor n : This defines n, the index of refraction.
34-2 Electromagnetic Waves The electromagnetic spectrum: