Electromagnetism · 06 / 06

Electromagnetic Waves

Light is not a separate substance added to electromagnetism. It is a traveling electromagnetic field: electric and magnetic components oscillating together while energy moves through space.

The learner question

How can fields keep traveling after leaving their original charges and currents behind?

A changing electric field is linked to magnetic change, and changing magnetic flux is linked to circulating electric field. In wave solutions, those coupled changes sustain a propagating disturbance.

Wave relationship
c=fλc=f\lambda
c=1μ0ϵ0c=\frac{1}{\sqrt{\mu_0\epsilon_0}}

Frequency and wavelength trade inversely while the wave speed in vacuum remains cc.

Coupled-field lab

See the same electromagnetic wave as two perpendicular field components.

Visible
electric field Emagnetic field Bpropagation →
frequency
550.00 THz
wavelength
545.08 nm
vacuum speed
2.998 × 10⁸ m/s
Frequency band10^14.7 Hz
Field amplitude1.00 ×
Wave phase0.18 cycle
wave idea
E and B are perpendicular

For an ideal plane wave in vacuum, the electric field, magnetic field, and propagation direction are mutually perpendicular.

wave idea
The spectrum is one phenomenon

Radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma radiation differ mainly in frequency and wavelength, not in their basic electromagnetic identity.

wave idea
No material medium is required

Mechanical waves need matter to oscillate. Electromagnetic waves are oscillations of the electromagnetic field itself and propagate through vacuum.

Maxwell synthesis

Now the four field laws form one dynamical theory.

Charge sources electric field. There are no observed magnetic monopoles. Changing magnetic flux curls electric field, while currents and changing electric flux curl magnetic field. Together, those relationships admit traveling electromagnetic waves.

Gauss — electric
nablacdotmathbfE=rho/epsilon0\\nabla\\cdot\\mathbf E=\\rho/\\epsilon_0
Gauss — magnetic
nablacdotmathbfB=0\\nabla\\cdot\\mathbf B=0
Faraday
nablatimesmathbfE=partialmathbfB/partialt\\nabla\\times\\mathbf E=-\\partial\\mathbf B/\\partial t
Ampère-Maxwell
nablatimesmathbfB=mu0mathbfJ+mu0epsilon0partialmathbfE/partialt\\nabla\\times\\mathbf B=\\mu_0\\mathbf J+\\mu_0\\epsilon_0\\partial\\mathbf E/\\partial t
Transfer check

The frequency of an electromagnetic wave in vacuum doubles. What happens to its wavelength?