Understanding the Potential of a Conducting Sphere Lowered into a Conducting Can

[conquerer7]

What do they mean when they refer to it? The PE of a system, I get, and the potential of a point is the work per unit charge needed to bring a charge there, assuming the charge has no effect on the field (right?).

A small conducting sphere originally has a charge +q. The sphere is lowered into a conducting can. Which of the following quantities are fixed as the sphere is lowered?
A. Potential of the can
B. Potential of the sphere
C. Charge on the sphere
D. Net charge on sphere and can

When they say 'potential of the can', do they mean the amount of work per unit charge needed to bring charge to its surface? If so, is that ignoring the contribution to the E field of the sphere? Is this potential relative to something? Relative to the sphere? Do they mean the potential energy in the sphere-can system?

Thanks for helping me sort this out!

 

[cepheid]

What do they mean when they refer to it? The PE of a system, I get, and the potential of a point is the work per unit charge needed to bring a charge there, assuming the charge has no effect on the field (right?).

A small conducting sphere originally has a charge +q. The sphere is lowered into a conducting can. Which of the following quantities are fixed as the sphere is lowered?
A. Potential of the can
B. Potential of the sphere
C. Charge on the sphere
D. Net charge on sphere and can

When they say 'potential of the can', do they mean the amount of work per unit charge needed to bring charge to its surface? If so, is that ignoring the contribution to the E field of the sphere? Is this potential relative to something? Relative to the sphere? Do they mean the potential energy in the sphere-can system?

Thanks for helping me sort this out!

The electric potential means what you think it means (i.e. it it defined at a point in space) It's just that these objects are conductors, which means that the potential has to be the same everywhere on them. Thus we can speak of the potential "of the can."

 

[conquerer7]

Alright, that makes sense. Is this reasoning right?

The potential of the can is raised, since negative charge moves to the inside to balance out the sphere's charge and positive charge moves to the outside. The can was at V = 0 previously because it was uncharged, but now V > 0.

The potential of the sphere is changed, but in an unpredictable way: the field it created is shielded by the can at points outside the can, but this field may be different.