Why doesn't the inside of a conducting cup transfer charge?

[mattwkeller]

Homework Statement

In a physics lab we were instructed to give a positive charge to a metal cup by induction. Once we acquired the charged cup we were told to touch the inside of a cup with a proof plane (small metal washer on a glass rod used to transfer charge). Next, we used an electroscope to find out if the inside of the cup would charge the proof plane. It did not. Next we touched the outside of the charged cup with the proof plane and used the electroscope to check its charge and it did charge the proof plane. Why is this? I'm assuming it has something to do with Faraday's discoveries with the ice bucket but I can't find a good explanation for this particular case. So if someone could explain this case (charged cup, neutral object) I would appreciate it.

Homework Equations

none?

The Attempt at a Solution

Im thinking it has something to do with vector quantities cancelling each other out to do the geometry of the cup, but i haven't a good explanation for this experiment. I am sorry if this isn't the right forum, this is actually my first post. If not i would appreciate some advice. Thanks

 

[andrevdh]

When you bend a charged sheet you are in fact bringing the charges closer together on the concave side of the sheet. So if it is an electrical conductor...

 

[mattwkeller]

I'm sorry I don't think I quite follow..does bringing them closer together make field strength smaller?

 

[andrevdh]

Just think in terms of the electric force.

 

[mattwkeller]

So F=kqQ/r^2 and E=kQ/r^2As the distance gets smaller the force and field strength increases. Is this what I'm supposed to be relating?

 

[gneill]

The cup is made of metal so any charges placed on it are mobile and are at the mercy of the electric forces acting between them. Do like charges attract or repel each other? How do you think the charges will distribute themselves?

 

[mattwkeller]

The charges would distribute equally throughout the metal, trying to get as far away from each other as possible...it would be a pattern that maximizes distance in between each charge.

 

[gneill]

The charges would distribute equally throughout the metal, trying to get as far away from each other as possible...it would be a pattern that maximizes distance in between each charge.

Really? Equally throughout the metal?

Do a thought experiment where you first place a single electron onto the cup (the cup starts out with no net charge, having equal numbers of electrons and protons comprising the metal). It feels no net force from the net neutral background, so it basically wanders around near where you put it on the cup. Now add a second electron somewhere on the cup. What happens? Where will they end up? How can they maximize their separation? Then add a third electron... and so on. Where do the charges end up?

 

[mattwkeller]

Oh, the electrons would end up forming a pattern the maximizes distance, but since they are repelling the would only end up on the outside of the cup. Correct?

 

[gneill]

Oh, the electrons would end up forming a pattern the maximizes distance, but since they are repelling the would only end up on the outside of the cup. Correct?

Bingo!

 

[mattwkeller]

So even when a conducting object is placed on the inside surface of the cup, it isn't enough to disrupt this electron formation? Just seems hard to believe that none of the charge transfers!

 

[gneill]

So even when a conducting object is placed on the inside surface of the cup, it isn't enough to disrupt this electron formation? Just seems hard to believe that none of the charge transfers!

If the conducting object is neutral (no net charge), then the other electrons won't even "see" it, as it exerts no electrical force to either attract or repel them. And since they're already "trying to escape" outwards due their own mutual repulsion, they're not going to move towards it.

 

[mattwkeller]

Ahh that makes sense. Thank you!

 

[gneill]

You're welcome.

Note that performing the simple thought experiment with just a couple or a few charges is often enough to get you thinking along the right path for these sorts of problems.