Question

prove that potential outside and inside the equopotential surface is same

Answer 1

Well, there are a number of reasons to prove that the surface of the conductor is equipotential . Simply consider that there have a potential difference between two points on the surface of a spherical conductor , then if a charge is placed on the higher potential point then it will immediately transfer to the lower potential point by nature and the charges accumulated the lowest potential point on the surface of the conductor. But in reality the charge uniformly spread all over the surface . Which proves that electric potential is constant on surface .
hope it will help you

Answer 2

hey mate ✨✨✨✨✨

follows:

When we apply Gauss's law to a charged conductor, we get to know that there is no electric field inside the conductor and all the charges reside in the surface of that particular conductor.

Electric field is equal to rate of change of potential and since electric field is zero therefore the potential across the surface of the conductor is constant.

hope it will help you ✨✨✨✨✌️