Electroscope Charge Distribution

[Livethefire]

Hey,

I am helping out with a class and the students were given a question about an electroscope that is being charged by induction, and they have to label the charge distribution on a diagram. The diagram is drawn such that the conductive elements are separated - indicating a force between them. The answer that is given is here:

Electroscope Induction

I have been getting the students thinking about the "sea" of electrons in the conducting rod and so some of them want to put positive charges on the top half and negative charges on the bottom half so that there is still a repulsion with net charge zero (no transfer/conduction). The more I think about it, the more I think they are not really wrong. I think the real answer lies inbetween that shown in the diagram, and that which I have described. Clearly if you bring a HIGHLY negative plate to the top, the students would be pretty much correct.

Does anyone wish to clarify this point(whether this is right or wrong), or add to the discussion?

Thanks.

 

[Simon Bridge]

I don't see the problem - the image shows positive charges on the top of the electroscope.
How do the student's answers differ from this one?

http://www.physicsclassroom.com/mmedia/estatics/esn.cfm

 

[Livethefire]

The student had something more like this:

The Upper "V" was positive, and the lower was negative. In otherwords half the rod was positive, the other was negative. This allowed the repulsion to still be correct.

 

[Simon Bridge]

Oh you mean the top part of the electroscope vane was positive and the lower negative?
That's fair enough - how would you go about determining the difference?

In practice you don't get a sharp change from positive to negative along a conductor like that. Can you find a charge distribution consistent with this setup that does not have the repulsion?

The question just wants the students to demonstrate that they understand the principles qualitatively.

 

[sardar]

I would like to confirm that the students' thinking about the "sea" of electrons in the conducting rod is correct. In an electroscope being charged by induction, the electrons in the conducting rod are repelled by the negatively charged object near the top of the electroscope. This results in a separation of charges within the electroscope, with the top half having a slight positive charge and the bottom half having a slight negative charge. This is known as a dipole moment.

However, it is important to note that this separation of charges is not a complete separation, as there are still some electrons present in both halves of the electroscope. This is why the net charge is still zero. So, while the students' thinking is partially correct, it is important to clarify that the charge distribution is not a complete separation of positive and negative charges.

Additionally, the strength of the repulsion between the conducting elements depends on the strength of the negatively charged object near the top of the electroscope. So, as the students mentioned, if a highly negative plate is brought near the top, the repulsion will be stronger and the separation of charges will be more evident.

I hope this clarifies the concept of charge distribution in an electroscope charged by induction. It is important for students to understand that charge distribution is not always a simple separation of positive and negative charges, but rather a more nuanced concept that depends on various factors.