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We know that divergence of Electrostatic field is

$$ \overrightarrow{\nabla}\cdot\overrightarrow{E}=\dfrac{\rho(\overrightarrow{r})}{\epsilon_0} $$

in case of a point charge, the divergence would be the Dirac-delta function.

What, similarly could be said about the curl at the location of point charge, we know that curl is zero for an electrostatic field , but that's at the points other than the location of the point charge.

If one tries to use Stoke's theorem to say that curl is zero everywhere, but Stoke's theorem requires that curl be define everywhere, how can we presume curl to be defined everywhere.

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  • $\begingroup$ Very related: physics.stackexchange.com/questions/168905/… $\endgroup$
    – user258881
    Commented May 31, 2020 at 8:21
  • $\begingroup$ i had read that before asking the question, it still doesn't answer me. What i am asking is , as there is discontinuity in Electric Field around the source point charge, it's divergence at the location of point charge comes out to be a delta function, as we would expect the derivatives to increase beyond all bounds. Similarly, what about the curl at the location of the point charge. $\endgroup$ Commented May 31, 2020 at 8:24
  • $\begingroup$ Try this discussion thread: physics.stackexchange.com/questions/126366/… $\endgroup$ Commented May 31, 2020 at 8:41

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Use Faraday's Law:

$$\nabla\times\mathbf{E}=\frac{\partial\mathbf{B}}{\partial t}$$

For a point charge at rest, we know that $\mathbf{B}=0$ everywhere, including at the location of the point charge. Thus $\frac{\partial\mathbf{B}}{\partial t}=\nabla\times\mathbf{E}=0$ everywhere, including at the location of the point charge.

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  • $\begingroup$ That's good , but can you, please, give me some resource to get the proof of Faraday's Law. $\endgroup$ Commented May 31, 2020 at 8:37
  • $\begingroup$ @uditnarayanpandey A proof starting from which axioms? $\endgroup$ Commented May 31, 2020 at 8:40
  • $\begingroup$ okay , i got you, thanks $\endgroup$ Commented May 31, 2020 at 8:48

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