Question

why is the potential inside a hollow spherical conductor constant and has the same value as on the surface?

Answer 1

Electric field is given by : E = -dV/dx = negative potential gradient.
potential is given by : V = -${\int }_{\infty }^{r}Edx$ = bring the charge from the infinity to that point.

Electric field inside the conductor is zero.(E_inside = 0)
Electric field outside is: E_outside = kq/r^​2

potential inside the conductor is given by: V = -${\int }_{\infty }^R$E_outsidedx - ${\int }_R^0$E_insidedx

= ​-${\int }_{\infty }^R$E_outsidedx = potential at the surface of the conductor

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where R is the radius of he conductor.