What is the Work Required to Charge a Spherical Shell?

In summary, the problem is to calculate the work required to charge a spherical shell with radius R and total charge Q. The solution involves using an integral, and the final answer is ke*Q^2/(2R). To approach the problem, one can consider the equivalence of work and energy and the change in electric potential energy when charging a sphere. The fact that it is a spherical shell also affects the problem.
  • #1
grief
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the problem is: "Calculate the work that must be done to charge a spherical shell of radius R and total charge Q", and I have no idea where to start. You probably have to write some sort of an integral but I don't know how. Can anyone give me a hint?
 
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  • #2
the answer, by the way is ke*Q^2/(2R), if that helps
 
  • #3
Think about the equivalence of work and energy, and the fact that charging a sphere changes the electric potential energy.
 
  • #4
I know that work is equal to the change of potential energy, but the potential energy of what? Won't it be just keQ/r^2. How does the fact that it is a spherical shell affect the problem?
 
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What is a spherical shell?

A spherical shell is a solid object with a spherical shape, similar to a ball, that is hollow on the inside.

How do you charge a spherical shell?

A spherical shell can be charged by rubbing it with a material such as silk or fur, by induction, or by using a charged object to transfer charge to the shell.

What happens when a spherical shell is charged?

When a spherical shell is charged, the charges distribute themselves evenly on the surface of the shell. This is known as the "Faraday's Ice Pail Experiment".

Can a spherical shell hold a charge on its surface?

Yes, a spherical shell can hold a charge on its surface. The charge will remain on the surface due to the repulsion of like charges and the shielding effect of the shell's surface.

How does the amount of charge on a spherical shell affect its electric field?

The amount of charge on a spherical shell does not affect its electric field inside the shell. However, the electric field outside the shell is affected by the total charge on the shell and the distance from the center of the shell.

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