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## Just a wave

In this post I continue exploring Maxwell’s insight regarding the nature of light as an electromagnetic wave.

Consider the solution to the wave equation:

is the direction of propagation of the wave and length equal to the wavenumber, is the angular frequency of the light.

Similarly,

Further,

So

and

Now looking at Maxwell’s equations in vacuo:

Hence the direction of propagation is orthogonal to both the direction of the electric field and magnetic field.

Now,

Hence,

Note ,

Finally,

Hence, the electric and magnetic field are orthogonal.

Insights from some symbolic manipulations…

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Categories: Mathematics

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