In 1865 James Clerk Maxwell brought together in four equations everything that was known about electricity and magnetism, added a missing term for mathematical consistency — the displacement current — and discovered that these equations naturally gave rise to electromagnetic waves travelling at the speed of light. Visible light, he deduced, is a particular electromagnetic wave: it was one of the greatest unifications in the history of physics. This chapter builds the equations one by one, derives the waves from them, and explores their energy, momentum, polarisation, sources (aerials) and the full spectrum.
Historical context — Maxwell, the (unjustly) forgotten physicist
Born in Scotland in 1831, James Clerk Maxwell published A Dynamical Theory of the Electromagnetic Field in 1865, presenting the celebrated equations. Einstein wrote of him: “In the life of every scientist there are few moments as perfect as when Maxwell understood that light was an electromagnetic wave.” And yet Maxwell is today far less well known than Einstein or Newton, partly because he died young, at 48, well before the importance of his work was fully recognised.
Sections
- The four equations (first, incomplete version)
- The capacitor paradox
- Maxwell’s correction: the displacement current
- Maxwell’s four equations (complete form)
- Speed of electromagnetic waves
- Structure of a plane electromagnetic wave
- Polarisation of electromagnetic waves
- Dipole aerial and generation of EM waves
- The electromagnetic spectrum
- The transformer