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there will be no tangential component of E^ in the case of the charged surface in electrostatics. If so then this would result in a force on the free electrons which would cause a drift hence a current which is not desired in electrostatics.


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The lighting shape and path is a non-linear phenomenon. Why? Because it involves a multitude of interactions with the medium (air molecules, atmosphere) and these depending on range of interecations are also non-linear. However there are compatibility conditions (or conserved quantities), as such this is a good example of the fractal geometry of nature.



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