## Maxwells synthesis 1061 Putting facts together

It is hardly surprising that, by the middle of the 19th century, the experimental results involving electrical and magnetic phenomena presented a complex and apparently disjointed picture. There seemed to be a lot of independent laws involving electric fields and currents, magnetic fields and induced currents. These were often quite complicated, with no logical connection between one law and another. In the year 1864, James Clerk Maxwell (1831-1879)

(The negative sign indicates that the direction of the induced E field is such as to oppose the change in magnetic flux. If this were not so, a self-sustaining chain of cause and effect would result in an exponential growth of energy without limit.)

put all the laws together and showed that in combination they form a beautiful unified picture. Maxwell realised that in essence there are only four laws in total: Gauss's theorem for electricity, Gauss's theorem for magnetism, Ampere's law and Faraday's law.

At that stage all four laws were very well established and had been confirmed by experiment. Maxwell expressed them as simultaneous equations — mathematical statements of facts which are all true at the same time — and could now use the power of mathematics to explore the consequences which follow from the four laws in combination.

The consequences were as surprising as they were dramatic. The solution of the equations showed how the interplay of electricity and magnetism gives rise to an electromagnetic signal which propagates at an enormous speed and provides a means of communicating information and transporting energy even across billions of miles of empty space. A new chapter had opened in the history of physics, with practical consequences of unimagined dimensions.

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