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Show that electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface.
Solution
Since $\vec{E}=0$ inside the conductor and has no tangential component on the surface no work is done in moving a small test charge within the conductor and on its surface.
That is there is no potential difference between any two point inside or on the surface of the conductor.
If the conductor is charged, electric field normal to the surface exises this means potential will be different for the surface and a point just outside the surface.
In a system of conductors of arbitrary size, shape and charge configuration each conductor is characterised by a constant value of potential but this constant may differ from one conductor to the other.
