Electric field and electric potential for spherical shell

Question

We know that electric field inside a spherical shell is 0 . But electric potential 'V' inside a spherical shell is kQ/R (Q = charge on the spherical shell and R = radius of the shell) We also know that V=Ed for D = distance of the point where we want to find the electric field or the potential . My doubt is that for thin spherical shell if we put the value of E= 0 , I.e. for a point inside the shell , then we will get V= 0 but from the formula above we are clearly not getting we = 0 , where am I mistaken ?

Answer 1

V=Ed

is only valid for constant or uniform electric field. The correct formula is $V=-\int \vec E.\vec {dl}$ .It gives potential difference and not absolute potential .The potential difference between any two points inside the shell is 0 but not their absolute potential.

Answer 2

The formula V = kQ/R gives the potential at the surface of a spherically symmetrical charge, Q, of radius, R (on the surface of your shell). It is found by integrating the, E, field in from infinity. As you point out, the, E, inside the shell is zero, so the potential does not change as you go in from the surface.