By far, the simplest explanation of Maxwell’s equations I’ve ever read is attached to Irregular Web Comic.
So you do the arithmetic. You take the values you measured for ?o and ?o, multiply them together, take the square root, and then take the reciprocal. The answer is a speed, so it has units of speed, in this case metres per second. And the answer is very close to 300,000,000 metres per second. Converted into miles, that’s a tad over 186,000 miles per second. Being James Clerk Maxwell, and a brilliant physicist, you immediately recognise what this number is.
The speed of light.
Where the heck did that come from??
You, James Clerk Maxwell, know in 1865 from the work of Isaac Newton and others that light has certain properties: that white light is composed of multiple colours of light mixed together; that transparent materials such as glass bends rays of light and can be used to focus them into images, such as in telescopes; and that light diffracts through small holes and around sharp edges. This diffraction property can only be explained by supposing that light is made of some sort of waves. But nobody in the world knows what sort of waves they are. Nobody knows what light actually is.
You stop.
Nobody in the world – except you – knows what light actually is.
When you were writing down your equations, you were thinking about electricity and magnetism. Light was the farthest thing from your mind. You had not the slightest clue (and nor did anyone else) that light was related to electricity or magnetism. But there it is, falling out of your equations.
You realise that you are the first person in all of history to know what light is made of. Can you imagine that feeling?
Maxwell’s equations gave humanity, finally, an understanding of what light actually is. His discovery was stunning and revolutionary. Light is electric and magnetic fields, wriggling through space together.
