Question

Why is static electric potential of the whole volume of the charged conductor equivalent to that on its surface?

Answer 1

Electric field inside whole volume of charged conductor is zero.
∵ E = \(-\frac{d V}{d r}\)
E = 0 ⇒ V = constant
(Electric potential is uniform in whole volume)
Inside conductor the work done in bringing any test charge from inside point to surface will be zero.
W = q₀(V_B – V_A)
V_B – V_A = 0
∴ V_A = V_B
Potential of both points will be equal.