Solving Electric Potential for q in Spherical Conductor

[stunner5000pt]

Homework Statement

A charge q sits in a spherical hollow inside a spherical conductor.

q is located at r=0
Hollow from r = 0 to r =a
from r=a to r=b a conductor
r=b to r = infinity free space

Find the potential everywhere
2. The attempt at a solution
I calculated these
$$E = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \hat{r}$$
for r<a and r> b

E= 0 for a<r<b


To find the potential from 0 to r=a is what concerns me... We end up having hte potential blow up in at the origin.

it is late and I am not thinking striaght but i can't see a way out ...

please help!

 

[chanvincent]

Your answer is correnct... Good job...

We end up having hte potential blow up in at the origin.

That is absolutely normal for a point charge, That is the reason why we have to
DEFINE V = 0 at r = infinity instead of r = 0