How can the electric potential of a dust grain in Saturn's rings be determined?

[Malgrif]

Homework Statement

Much of the material making up Saturn's rings is in the form of tiny dust grains having radii on the order of 10^-6 these grains are located in a region containing a dilute ionized gas, and they pick up excess electrons. As an approximation suppose each grain is sphereical, with radius R=1.0*10^-6m. How many electrons would one grain have to pick up to have a potential of -400V on its surface. (taking V=0 at infinity)?

Homework Equations

V=U/q
V=-W/q

The Attempt at a Solution

not quite sure where to start. I think V=-400=U/q but I don't know how to get U. I'd like to understand why U is relevant in this question also. Thanks

 

[SammyS]

What is the electric potential of a conducting sphere of radius r and charge Q ?

 

[Malgrif]

What is the electric potential of a conducting sphere of radius r and charge Q ?

oh alright. is there another way to solve that problem without relying on that though. That equation is presented in a later section and the question is presented with only knowledge of potential energy and electric potential assumed.