## Maxwells electromagnetic waves

James Clerk Maxwell

Another piece of evidence in support of the wave nature of light came from the theoretical work of James Clerk Maxwell (1831-1879). Maxwell put together laws of electricity and magnetism which had been discovered by Karl Gauss (17771855), Andre Ampère (1775-1836) and Michael Faraday (1791-1867). These laws were, in Maxwell's time, well established but were considered as separate and independent. Maxwell's achievement was to unify phenomena in electrostatics, magnetism and current electricity by expressing the laws mathematically, in the form of four simultaneous differential equations.

The experimental evidence which Maxwell synthesised:

1. Coulomb's law, which describes the force exerted on one another by electric charges at rest. It can be expressed mathematically in another form called Gauss's theorem.

2. Gauss's theorem, applied to magnetism, expresses the fact that magnetic monopoles do not exist.

3. Ampère's discovery that an electric charge in motion produces a magnetic field.

4. Faraday's discovery that a changing magnetic field produces an electric field. Maxwell extended the symmetry

James Clerk Maxwell

to a changing electric field in turn producing a magnetic field.

The equations describing these laws must all be true at the same time (they are simultaneous equations). When Maxwell put the four equations together, and solved them, he established the consequences of the four laws being true at the same time. The result was a prediction that by accelerating an electric charge, one would create a signal which would propagate through space: An oscillating charge would give rise to an electromagnetic wave, travelling through space at a fixed speed. Maxwell was able to calculate this speed, and obtained an answer practically identical to the measured speed of light. This could hardly be a coincidence. Light must be an electromagnetic wave.

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