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I have a doubt in electordynamics,
I was learning Electrodynamics (last major topic) , and I learned about Maxwell's Equation, which can explain everything in Electrodynamics (actually according to my book).

So, can we derive everything of electrostatics (for now) using just Gauss Law ...

I was able to derives Electric field due to a single particle using it ,

after that I think we can derive everything if we are able to show Superposition principle of Electric Field lines .

Is there is any way to do it ?

Or I am getting something wrong ?

Please help , any help will be appreciated..

gandalf61
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MathSolver
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1 Answers1

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Your question is not so well-defined, thus not sure whether the following can be considered and answer.. Anyhow, one can show the following: The 'simplest' equations that satisfy

  • Superposition principle (basically meaning the set of equations must be linear).
  • Lorentz covariance (meaning all entities in the equations must transform as they should if frame of reference is changed).
  • A point source (in the rest frame) obeys Gauss law.
  • Electric charge is conserved
  • There is no magnetic charge

are the Maxwell equations. The 'proof' is not that difficult, but you should be familiar with the covariant of formulation of the Maxwell equations, like $\partial_{\mu} F^{\mu\nu} = j^{\nu}$ from which e.g. follows that $F$ must be an antisymmetric tensorfield if electric charge is to be conserved.

alain
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