Homework Help: Finding radius a of non-conducting spherical shell

1. Jun 12, 2012

Ryomega

1. The problem statement, all variables and given/known data

A non-conducting spherical shell is uniformly charged.
The electrostatic potential $\phi$ at the centre of the sphere is $\phi$1 = 200V
The potential at distance r = 50cm from the centre is $\phi$2 = 40V
Find the radius of sphere: a

2. Relevant equations

I seem to have missed this lecture.

3. The attempt at a solution

I understand that the potential (V) is a function of r (distance from centre) and satisfies:

V(0) = 200V
V(50) = 40V
V(a) = 0V

I've been reading up on this, but I can't seem to make sense out of this question. I can't seem to find a case for non conducting spherical shell. Would someone mind providing me a formula and clear steps to solve this problem?

Thank you!

2. Jun 12, 2012

HallsofIvy

The "non-conducting" just means that you don't have to worry about the charge moving! Yes, V is a function of r- more specifically it is $C/r^2$.

So you have $C/r^2= 200$ and $C/(r- 40)^2= 40$, two equations you can solve for C and r.

Since you really only want to solve for r, I would recommending dividing one equation by another to eliminate C.

3. Jun 13, 2012

Ryomega

Thanks for the quick reply!!! I understand how to do the question now. is C just some constant? Or is it charge (Q)?

Not that it matters in this question but I'm certain I need to know this for other stuff.

Thanks again!!!

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