What Happens to the Charge Distribution When Separating Two Metal Spheres?

[ikihi]

Homework Statement

X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X. Sphere Y is then physically moved away from X. What are the final charge states of X and Y?

Homework Equations

N/A

The Attempt at a Solution

I think X is negative and Y is positive. Can anyone elaborate on why this may be?

 

[hilbert2]

Use Coulomb's law to show that the electrostatic potential energy of the system is smaller if X is negative in the final state.

 

[gneill]

I think X is negative and Y is positive. Can anyone elaborate on why this may be?

Why don't you start by explaining your initial reasoning? Why do you think that X ends up negatively charged and Y positively charged? What concepts are involved?

 

[ikihi]

Why don't you start by explaining your initial reasoning? Why do you think that X ends up negatively charged and Y positively charged? What concepts are involved?

Not totally sure, but my guess is:
When the positive rod is brought close to X which is touching Y, positive charges are pushed away from the rod across sphere X and onto sphere Y. Now X has more negative charges (electrons) and thus has a negative charge. The positive charge that was pushed onto Y give it an overall positive charge.

 

[gneill]

Not totally sure, but my guess is:
When the positive rod is brought close to X which is touching Y, positive charges are pushed away from the rod across sphere X and onto sphere Y. Now X has more negative charges (electrons) and thus has a negative charge. The positive charge that was pushed onto Y give it an overall positive charge.

Okay, that's a reasonable interpretation. How might you modify it if you were to assume that the only mobile charges are negative ones (electrons), and that any positive charges (atomic nuclei) are immobile?

 

[ikihi]

Okay, that's a reasonable interpretation. How might you modify it if you were to assume that the only mobile charges are negative ones (electrons), and that any positive charges (atomic nuclei) are immobile?

Bringing the positive rod towards the X-sphere, would make the X-sphere positively charged and thus draw the elections away from the Y-sphere leaving it positively charged and leaving the X sphere with an excess of negatively charged elections?

 

[gneill]

Bringing the positive rod towards the X-sphere, would make the X-sphere positively charged and thus draw the elections away from the Y-sphere leaving it positively charged and leaving the X sphere with an excess of negatively charged elections?

Almost. Leave out the the phrase "would make the X-sphere positively charged". The positive rod in close proximity to the X sphere is enough to draw electrons from both spheres towards the rod. The X-sphere in fact gains an overall negative charge with the excess electrons that gather there.

 

[ikihi]

Almost. Leave out the the phrase "would make the X-sphere positively charged". The positive rod in close proximity to the X sphere is enough to draw electrons from both spheres towards the rod. The X-sphere in fact gains an overall negative charge with the excess electrons that gather there.

Ah I see, Thanks. So the answer would be: "Bringing the positive rod towards the X-sphere draws electrons from both spheres towards the positive rod. The electrons gather onto sphere X, leaving sphere Y with a net positive charge due to the loss of electrons onto sphere X."

 

[gneill]

Right. Then you should mention the consequences of separating the spheres at that point.