**Required math: algebra**

**Required physics: special relativity**

Reference: Moore, Thomas A., *A General Relativity Workbook*, University Science Books (2013) – Chapter 7; Problems 7.1.

Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Problem 12.48.

To apply this to Griffiths problem 12.48, use

in place of in what follows. The results are the same.

The electromagnetic field tensor is

We can use the usual tensor transformation rules to see how the electric and magnetic fields transform under a Lorentz transformation. We get

where the Lorentz transformation matrix is

As we saw when discussing the inertia tensor, we can write this transformation as a matrix equation

The first product is

The final product is

Using we get

From this, we see that

Unlike lengths, the components of and in the direction of motion are unchanged, while those perpendicular to the motion are altered.

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PeterI’m not sure, but I think that the last expression of B’z should be = -γβEy + γBz and B’y = γβEz + γBy

In any case the article was really useful, thank you for that!

growescienceQuite right – fixed now.

Anonymous“The first product is:

\Lambda F = [Matrix]”

But the first element of the second line is $+\gamma E_x$, and not $-\gamma E_x$

growescienceElement in equation 6 is calculated from the second row of multiplied into the first column of , which gives , so it’s correct as it is.

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