Maxwell equation are derived in which coordinate system

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SUMMARY

The discussion centers on the derivation of Maxwell's equations in various coordinate systems, emphasizing that these equations are valid in all inertial reference frames as a consequence of special relativity. Participants noted that in classical electrodynamics, particularly when solving the Poisson equation, the choice of origin and axes does not affect the validity of Maxwell's equations. The Michelson-Morley experiment is highlighted as a significant historical attempt to find deviations from these equations in different reference frames, ultimately confirming their consistency across inertial systems. The conversation also touches on the mathematical aspects of curl and divergence in relation to coordinate transformations.

PREREQUISITES
  • Understanding of Maxwell's equations and their implications in electrodynamics.
  • Familiarity with coordinate systems and transformations in physics.
  • Basic knowledge of curl and divergence in vector calculus.
  • Awareness of the Michelson-Morley experiment and its significance in physics.
NEXT STEPS
  • Explore the mathematical derivation of Maxwell's equations in different coordinate systems.
  • Study the implications of special relativity on classical physics, particularly in relation to Maxwell's equations.
  • Investigate the role of curl and divergence in vector fields and their applications in electromagnetism.
  • Review the historical context and findings of the Michelson-Morley experiment.
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Physicists, electrical engineers, and students studying electromagnetism or special relativity, particularly those interested in the mathematical foundations of Maxwell's equations and their applications in various coordinate systems.

Matt Smith
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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.
 
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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.
 
Any inertial coordinate system will do
 
mfb said:
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.
 
Matt Smith said:
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?
 

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