Question

Why is electrostatic potential constant throughout the volume of the conductor and has the same value inside?

Answer 1

Electrostatic potential:

1. The amount of work that is done in order to move a unit charge from a reference point to a specific point inside the field without producing an acceleration is called electrostatic potential.
2. . When there is no current inside or on the surface of the conductor, the free charges have distributed themselves so the electric field is zero everywhere inside the conductor. The electrostatic field is zero inside a conductor.
3. Since there is no electric field inside the conductor, the potential there must be identical to the potential outside.

It is understood that the relation between electric field and potential is:

$E=-\frac{∆V}{∆d}$

So,

$\begin{array}{rcl}0& =& \frac{∆V}{∆d}\\ ∆V& =& 0\\ V_1-V_2& =& 0\\ V_1& =& V_2\end{array}$

Here,

$V_1,V_2$ is the electric potential at different points inside the conductor.

Hence, the potential inside the conductor is the same at all points.