How does Coulomb's law change in 3+1 dimensional spacetime?

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SUMMARY

Coulomb's law is expressed as $$1/r^{n-1}$$, where n represents the spatial dimension. In three dimensions (n=3), this results in the inverse square law. When considering a 3+1 dimensional spacetime, the law remains applicable for static charges but requires modification through Maxwell's equations to account for time-varying fields. Thus, while the fundamental form of Coulomb's law persists, its application in dynamic scenarios necessitates a transition to a more comprehensive framework.

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jk22
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The power law of Coulomb depends on the dimension treated . It is $$1/r^{n-1} $$ where n is the dimension.

In n=3 we get the inverse square law.

How does this go into considering now spacetime 3+1 dimensional ? Would it modify the law and how ?
 
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The Coulomb law is only valid for a single static charge. The static solution is three-dimensional as it does not depend on time. To deal with time changing fields you need Maxwell's equations.
 

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