Maxwell equation are derived in which coordinate system

[Matt Smith]

Ignoring special relativity theory，maxwell equation are deduced in which coordinate system?In most electrodynamics textbook,maxwell equation are deduced without specifying which coordinate we are using.For example,when we are solving poisson equation in static case，it seems we can freely choose the original point,and 3 direction without contradict maxwell equation.It seems when we are deducting maxwell equation ,there are many equivlent coordinate system in which maxwell equation holds.When we are developing special relativity theory,we want to find the coordinate system in which maxwell equation holds,or in which system light have speed c.But it seems weird because we should know this coordinate system for a long time,because it should be the coordinate system in which we observe the electromagnetism phenomenon and deduce maxwell equation.

 

[mfb]

The Maxwell equations are valid in all (inertial) reference frames. This is a result of special relativity. In Newtonian physics there must be deviations from the Maxwell equations in some reference frames - people searched for it but didn't find a deviation. Today we know why. The Michelson-Morley experiment is the most prominent example of an experiment that looked for deviations.

 

[Dale]

Any inertial coordinate system will do

 

[Matt Smith]

The Maxwell equations are valid in all (inertial) reference frames. This is a result of special relativity. In Newtonian physics there must be deviations from the Maxwell equations in some reference frames - people searched for it but didn't find a deviation. Today we know why. The Michelson-Morley experiment is the most prominent example of an experiment that looked for deviations.

I just want to know when we solve differential equation ,why choosing a different original point and axes won't make any difference.Curl and divergence rely on the x,y,z.So please ingore the relativity chapter in Jackson's book or griffiths,and take chapter3,or 4 as an example.In the first several chapter we never mention the reference frame but with a lot of using curl and divergence.So in the first several chapter,when we do partial differentiation,we are doing it relative to which"x,y,z"?It is not a problem about relativity.

 

[Dale]

why choosing a different original point and axes won't make any difference.Curl and divergence rely on the x,y,z.

This is just straight math. You should work this out for yourself. Transform from some T, X, Y, Z coordinate system to
T=t+t0
X=x+x0
Etc.
Substitute into Maxwell’s equations and simplify. What do you get?