Faraday’s lines acquired mathematics

Faraday imagined electric and magnetic influence distributed through space as fields. James Clerk Maxwell translated that physical picture into equations and added one crucial term: a changing electric field can produce a magnetic field, even where no wire carries current.

With that addition, the equations sustain traveling disturbances. Electric and magnetic fields regenerate one another as they move.

Electromagnetic-wave propagation Scientific model diagram E E B B E ⟂ B ⟂ c λ = λ E ⟂ B ⟂ c λ = λ propagation c propagation c
Edit in Studio
Diagram description

Static physics diagram: maxwells_electromagnetic_wave.

The speed gave away the wave

The predicted speed was

c=1μ0ε0,c=\frac{1}{\sqrt{\mu_0\varepsilon_0}},

and available electrical measurements made it strikingly close to the measured speed of light.

Maxwell concluded that light itself is an electromagnetic wave. Optics was no longer a separate subject sitting beside electricity and magnetism.

No one had asked the equations to explain light. The identity emerged because two independently measured constants combined into a familiar speed. A successful unification does more than shorten a textbook. It makes one part of nature unexpectedly answer a question posed in another.