Prove that inside a conductor all points have the same potential, equal to the potential on the surface of this conductor?

Free charges cease to move along the surface of a conducting body when their distribution is reached such that the vector of the electric field strength at any point is perpendicular to the field surface. Therefore, in an electric field, the surface of a conducting body of any shape is an equipotential surface.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.