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why is electrostatic potential constant throughout the volume of the conductor and has the same value(as inside) on its surface??

see the equation V=1/4piepsilonzero*q/r

here every term except r is constant..for any point on a suraface for eg;spherical surface r that is radius remains same..so it remains constant

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 as electric field inside the conductor is zero so there is no work done in moving a small test charge within the conductor.therefore there is no potential difference between any two points inside the conductor that is electrostatic potential is constant throughout the volume of the conductor.

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E=-dV/dr

Where E is the electric field and v is the potential and r is the distance.

Since inside a conductor the E field is zero.

=>0=-dV/dr

=>dV=0 i.e the change in potential inside the conductor is a constant.

And this value is k Q/r where k is the constant and Q is the Charge on the surface of the conductor.

And r is the radius.
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