electrostatics- work done related question A point charge $q$ is at the center of an uncharged spherical conducting shell of inner radius $a$ and outer radius $b$. How much work would it take to move the charge out to infinity (through a tiny hole drilled in the shell)? I could not understand the question. Please help me solve this out. 
 A: You just need to find out the potential at the center of the shell. Work required to take the charge to infinity is simply negative of that potential assuming zero potential at infinity.
The shell is made of conductive material which means all the charge will accumulate at surface. If you imagine a spherical gaussian surface of radius $R$ such that $$a<R<b$$
Flux through this surface is zero because electric field inside a conductor is zero. This implies that net charge inside the region enclosed by the gaussian surface is zero. So, charge accumulated at the inner surface of the conductor is $-q$ and by conservation of charge for conductive sphere, charge accumulated on outer surface is $+q$
I think I have simplified the problem enough for you to be able to solve it. You just have to calculate potential due to the two surfaces, you can assume these surfaces to be thin shells with uniform charge. If you don't know about gauss's law or conductor's properties, then I suggest that you go through the theory before attempting problems.
