Simple charging by induction problem

[awvvu]

Homework Statement

A small positively charged sphere is lowered by a nonconducting thread into a grounded metal cup without touching the inside surface of the cup. The grounding wire attached to the outside surface is disconnected and the charged sphere is then removed from the cup. What best describes the subsequent distribution of excess charge on the surface of the cup?

The Attempt at a Solution

It's a multiple choice question and the answer is "Negative charge resides on the outside surface, and no charge resides on the inside surface."

I don't understand why no charge is in the inside surface though.

1. Sphere polarizes cup and ground. Cup is charged negative and ground is "positive".
2. Ground removed. Negative charges are isolated on cup.
3. Charges move to exterior surface of the conductor.

Doesn't the "exterior surface of the conductor" include the inside surface of the cup as well as the outside surface?

 

[Chi Meson]

A general rule: all net charge resides on the exterior of a conducting surface. Since the cup was grounded when the charged sphere was introduced, electrons from the outer surface were pulled to the inside of the sphere. "Replacement" electrons were pulled onto the cup through the grounding wire. Wire is removed, and charged sphere removed. There are now "excess electrons" on the cup. With no outside influence, those electrons will be pushing away from each other. This will cause them to reside on the outside, the furthest away they can get from each other, and thereby the lowest state of energy.

and "exterior" means "outside." Interior surface would be the inside surface. There is no ambiguity with the statement.

 

[Moetasim]

I would say that the subsequent distribution of charge on the surface of the cup is a result of the process of induction. When the positively charged sphere is lowered into the cup, it polarizes the cup and the ground, causing a redistribution of charges. The negative charges on the cup's surface are attracted to the positive charge of the sphere, leaving the inside surface of the cup with a net positive charge.

When the grounding wire is disconnected and the charged sphere is removed, the negative charges on the inside surface of the cup are no longer attracted to the positive charge of the sphere and are free to move. However, due to the non-conducting thread and the non-conducting nature of the cup, these negative charges cannot move to the outside surface of the cup. Therefore, the excess charge on the inside surface of the cup remains isolated and the outside surface of the cup remains with no net charge.

In summary, the subsequent distribution of excess charge on the surface of the cup is due to the process of induction and the non-conducting nature of the cup and thread, which prevent the charges from fully redistributing to the outside surface.