# Homework Help: Potential of the inner earthed sphere

1. Feb 10, 2010

### twinklestar10

1. The problem statement, all variables and given/known data
An outer shell of charge +Q is insulated by a light thread. There is an inner sphere inside which is earthed. The radii of the outer shell and inner sphere are b and a respectively. What is the potential of a point which is at a distance r from the centre of the inner sphere, where
(i) r=b?
(ii) r=a?

2. Relevant equations
V at r = - $$\int charge/ (4\pi\epsilon r^{2})$$ from infinity to r

3. The attempt at a solution
Before answering the questions above, I find it difficult to calculate the amount of induced charge on the inner sphere... Because the outer shell having a charge of +Q doesn't mean that the inner shell must have an induced charge of -Q.

How can I find the amount of induced charge?
My teacher gave us some hints to solve this question:
the inner sphere is an open system as it is earthed
the amount of charge of the inner sphere can be calculated

Besides, I initially thought the potential must be 0 without calculation because it is earthed, but when I tried to do the integration (V = dE/ dr), I couldn't get it as 0 (maybe it's due to the problem that I couldn't find the amount of induced charge of the inner sphere)

Can anyone help me?

thanks!

Last edited: Feb 10, 2010
2. Feb 10, 2010

### ideasrule

The inner earthed sphere must have a potential of 0, because it's earthed. That means the potential of the two spheres' center must also be 0, since there's no electric field inside the inner sphere.

3. Feb 10, 2010

### twinklestar10

but how to prove it using mathematical calculations? i couldn't get it as 0 using the integration of electric field with respect to r.