# Work done, conducting shell

• NT123
In summary, to find the work done to move a test charge from the origin to the edge of a spherical conducting shell, use the equation W = int(F.ds), where W is the work done, F is the force, and ds is the distance moved. At the origin, the force cancels out due to equal amounts from each radial direction. Beyond the origin, Gauss' Law states that the field inside the spherical shell is zero. The correct answer for the work done is given by (1/4*pi*epsilon0)*(q^2)/R, where R is the radius of the shell.
NT123

## Homework Statement

Find the work done to move a test charge with charge q from the origin to the edge of a spherical conducting shell which surrounds it, also of charge q. (Shell is of radius R).

## Homework Equations

W = int(F.ds) where W = work done, F = force

## The Attempt at a Solution

I would have thought that at the origin the force cancels out since there is an equal amount from each radial direction. Beyond this however I am not sure what to do... I tried the overall answer

(1/4*pi*epsilon0)*(q^2)/R where R is the radius of the shell, but that was incorrect. Any help would be appreciated.

Ignoring the test charge, what does Gauss' Law say about the field inside the spherical shell?

## 1. What is work done?

Work done refers to the amount of energy transferred to or from an object when a force is applied to move it a certain distance. It is measured in joules (J).

## 2. How is work done calculated?

The formula for calculating work done is W = F x d, where W is the work done, F is the force applied, and d is the distance moved in the direction of the force.

## 3. What is a conducting shell?

A conducting shell is a hollow, metallic object that is capable of conducting electricity. It is typically made of a material such as copper or aluminum and is used to enclose or shield electrical components or circuits.

## 4. How does a conducting shell affect work done?

A conducting shell does not directly affect the work done on an object. However, it can affect the electric field and potential inside the shell, which can in turn affect the work done on a charged object inside the shell.

## 5. What is the relationship between work done and conducting shells?

The relationship between work done and conducting shells is that the electric potential inside a conducting shell is constant. This means that the work done on a charged object inside the shell is independent of its position, as long as it remains within the shell.

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