Potential of the inner earthed sphere

[twinklestar10]

Homework Statement

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?

Homework Equations

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

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!

 

[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.

 

[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.