Finding radius a of non-conducting spherical shell

[Ryomega]

Homework Statement

A non-conducting spherical shell is uniformly charged.
The electrostatic potential \phi at the centre of the sphere is \phi₁ = 200V
The potential at distance r = 50cm from the centre is \phi₂ = 40V
Find the radius of sphere: a

Homework Equations

I seem to have missed this lecture.

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!

 

[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.

 

[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!