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but what about other surfaces, say the surface which are not equipotential?

This is my first question.

ok, now

as [tex]grad \phi[/tex] is a vector normal to surface it cant be 0. Because that would mean that surface have no normal vector, or say a normal vector of indeterminate direction (as 0 vector is of indeterminate direction). how can it be possible that a surface has no normal vector, more specifically a 0 vector as its normal vector?

But I have seen many examples in which [tex]grad \phi[/tex] is 0.

So doesn't that contradicts the assumption that [tex]grad \phi[/tex] is a normal vector?