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I have recently come across this topic of equipotential surfaces. I have a very basic doubt:

Q.) Let's say we are talking about a point P inside the equipotential surface(eg:sphere). Now, before considering the equipotential surface let's beforehand calculate the potential at point P. After calculating, condsider the equipotential surface. And potential on surface = potential inside surface (in walter lewins video). So ofcourse now the potential which we calculated before wouldn't be the same after drawing equipotential surface. So, how did the potential inside change by just drawing a surface ?

Walter Lewins video, [16:25 - 16:55], he clearly says that potential on surface is same as anywhere inside.

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He has not just drawn a surface in space, he is talking about an actual shell of metal with a uniform charge on it. From Gauss, the electric field anywhere inside a closed spherical shell like this is zero. Therefore, since $E = \nabla V$, the potential must be constant throughout and equal to the potential of the shell.

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