Moving a point charge out of a cavity in a conductor

[Momentous]

Homework Statement

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
innity? (find the minimum work needed. Assume charge can take out through a tiny hole
drilled in the shell. Think about the work you need to assemble the system)

Homework Equations

W = qV
V = ∫E. dl
dl = (r^ dr + θ^ dθ + ϕ^ d ϕ)

The Attempt at a Solution

The overall equation is W = qV. I'm just a little unsure about getting V (q is given).

My guess is that there has to be two integrations for the Voltage inside and outside of the shell. I'm not really too sure about all of that, because isn't the Voltage in a conductor always constant.

So is it possible V = (V(out) + V(in)) = (V(out) + C) where C is just some arbitrary constant. Or can you actually find the constant value of that voltage with the information given?

 

[Dick]

Homework Statement

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
innity? (find the minimum work needed. Assume charge can take out through a tiny hole
drilled in the shell. Think about the work you need to assemble the system)

Homework Equations

W = qV
V = ∫E. dl
dl = (r^ dr + θ^ dθ + ϕ^ d ϕ)

The Attempt at a Solution

The overall equation is W = qV. I'm just a little unsure about getting V (q is given).

My guess is that there has to be two integrations for the Voltage inside and outside of the shell. I'm not really too sure about all of that, because isn't the Voltage in a conductor always constant.

So is it possible V = (V(out) + V(in)) = (V(out) + C) where C is just some arbitrary constant. Or can you actually find the constant value of that voltage with the information given?

I would think about using your E.dl form instead. To find E at the point where the charge is use the method of image charges. Have you covered that topic?

 

[Momentous]

I can't say that I know what that method is. Isn't my method using the E.dl form?