Moving a point charge out of a cavity in a conductor

AI Thread Summary
To determine the work required to move a point charge from the center of a spherical conducting shell to infinity, the relevant equation is W = qV, where V is the voltage. The discussion highlights confusion regarding the calculation of voltage, particularly whether it requires separate integrations for the inside and outside of the shell. It is noted that the voltage within a conductor is constant, leading to questions about how to express the total voltage. The method of image charges is suggested as a potential approach to find the electric field at the charge's location. Understanding these concepts is essential for accurately calculating the work needed.
Momentous
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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?
 
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Momentous said:

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

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