Calculating voltage within and outside of a solid sphere

[starstruck_]

Homework Statement

A solid sphere with radius R=12 m has charge Q=3 nC distributed uniformly throughout its volume.
(a) Calculate the potential difference between a location at infinity and a location on the sphere’s surface.
(b) Calculate the potential difference between a location on the sphere’s surface and the location at the sphere’s centre.

Homework Equations

V= ∫ E.R (both vectors)

V= kq1q2/r

The Attempt at a Solution

I'm struggling with understanding this unit in general (first year physics- teacher in high school did not teach electricity) so if I could get some help with this question, it might make the unit in general much clearer for me.

This is what I think:

For part A, I'm integrating between the surface of the sphere and infinity - the force at a distance of infinity is negligible so I'm going to assume 0 for it (prof says it's okay to do so).

so if I'm integrating between infinity and the surface, my integral's upper limit would be ∞ and the lower limit would be R (radius of the sphere).

Since Q is distributed evenly around the volume, I would divide Q by the volume at R; so

_R^∞∫k3Q/4πR³? I'm not sure if this is right or let alone whether I'm on the right track.

As for Part B, I would do the same thing but between R and r? Volume would be a factor as the gaussian spheres inside the sphere would have a different amount of charge depending on their volume (as the radius increases) ??

 

[haruspex]

Since Q is distributed evenly around the volume, I would divide Q by the volume at R; so

_R^∞∫k3Q/4πR³?

You need to understand what you are effectively calculating there.
Dividing by the volume gives the charge density inside the sphere. This is a constant. Your integral is undefined because you have not specified the variable of integration (the "dx"). It cannot be R because R is a constant.
Anyway, there does not seem to be any value in integrating the charge density within the sphere over a range outside it.

What do you know about the field outside a uniformly charged spherical shell?