EasyPhysicsHigh School (11–12)Electricity & Magnetism › Electric Potential and CapacitanceConceptualA-LevelAPIB
A neutral, hollow metal can stands on an insulating stand…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A neutral, hollow metal can stands on an insulating stand. A small ball with a charge of nC is lowered into it on a silk thread, without touching the can. Say what charge is on the inner wall and on the outer wall of the can. Then the outside of the can is joined to the earth for a moment, and the wire is removed. What charge is on the outer wall now, and is there a field outside the can?
Need a reminder? The key ideaShow
In a conductor at rest the field inside is zero and the extra charge sits on the surface. Just outside, , with . A ball of radius with charge has the potential and the field at its surface, with . Joined spheres share the charge in the ratio of the radii. In a dielectric and the bound charge has .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Before earthing. The field in the metal is zero, so every field line from the ball ends on the inner wall. The inner wall carries nC. The can is neutral, so nC is left on the outer wall.
Step 2. After earthing. The earth takes the charge of the outer wall, so the outer wall becomes neutral. The inner wall keeps nC, because the ball still pulls on it. The total charge of the can is now nC.
Step 3. The field outside. With no charge on the outer wall, there is no field outside the can. The ball is shielded, and the can is a closed shell round it.
Watch out. The ball is still charged. Only its field is hidden from the outside. If the ball is taken out, the can is left with nC and now shows a field.
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