Homework 13 Answers, 95.658 Spring 2011, Electromagnetic Theory II
Dr. Christopher S. Baird, UMass Lowell
Problem 1
Show that Maxwell's equations obey Einstein's special relativity. Assume we have already proved that
the electromagnetic field strength tensor is indeed covariant and transforms from one frame to another
according to Lorentz transformations. Take the Maxwell equations in vacuum as written in covariant
form, Lorentz transform each piece of each equation to the new frame using covariant notation, and
simplify the equations to their original form.
SOLUTION:
Assuming we have proven that the electromagnetic field strength tensor is covariant, we know it
transforms like a typical covariant tensor:
F
'
=
F
In covariant notation, Maxwell's equations are:
∂
'
F
'
=
4
c
J
'
and
∂
'
F
'
=
0
Let us now Lorentz transform the derivative 4vector and the current 4vector to the
K
frame:
∂
F
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 Spring '11
 Staff
 Mass, Work, Special Relativity, Magnetic Field, Lorentz, field strength tensor, electromagnetic ﬁeld strength

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