Electric force and electrons transfered

[NihalRi]

Homework Statement

In a group assignment we had to find out how many electrons were transferred to pieces of tape after we pealed them of a table.

The second part of the project asked us to imagine that one piece of tape was a distributed charge and that the other was still a point charge.

Homework Equations

F=kqq/r^2
F=mg
E= kq/(x(x^2+(L/2)^2)^(1/2))

The Attempt at a Solution

We imagined that these two tapes were represented by point charges located at the center of each tape for the first project.

our teacher said this method had a problem but I still can't see anything wrong, I would appreciate some help identifying the problem.

For the second part of the project I thought that we could use the electric field expression for distributed charge of a rod we derived in class to represent one of the tapes. The only problem is that the tape also has a noticeable width. For this project the only things we could use were expressions we had already derived for electric field of a :
a. Dipole

b. Set of a finite number of point charges

c. A uniformly charged rod

d. A uniformly charged ring

e. A uniformly charged disk

f. A solid sphere uniformly charged throughout its volume

g. A spherical shell with a uniformly charged surface

Would any of these be more suitable than the rod expression.
Thanks in advance for the help.

 

[Simon Bridge]

Please describe the method used in words - and explain the physics behind it as you understand it.

 

[haruspex]

... in particular, please describe the physical set-up of the tapes in a way that makes the relationship to the diagrams clear. What, for example, is the angle theta the angle between?

 

[NihalRi]

Please describe the method used in words - and explain the physics behind it as you understand it.

Just after the tapes start to get attracted to each other, we can say that the system in in equilibrium because nothing is moving. The force of gravity acts downwards and the electric force acts towards the side. The tension force counters both these forces and it's vertical and horizontal component is equal an opposite to the other two forces mentioned. We know that the downward force is of gravity = mg and thus the vertical component of the tension force.

angle theta the angle between?

If we know the angle between the vertical and the direction of the tension force at the center of the tape, we can calculate the horizontal component using trigonometry(tan) in terms of mg(=mgtanθ). At this point we are imagining both tapes are represented by point charges located at the center of each tape. The magnitude of this horizontal force is equal to the magnitude of the horizontal electric force(kqq/r^2). Now these two different expressions for the force can be equated and re-arranged to make q the subject. Since we experimentally found all the other variables in the equation we could just plug in the values to solve for q, which is the total charge transferred to one tape. dividing this by the charge of e gave us an estimation of the number of electrons transferred.

For the second part of the project I ended up just going with the charge distribution model of a rod. The only thing that changes was the expression for the electric force which is given by E= kq/(x(x^2+(L/2)^2)^(1/2)) multiplied by q. This is the force between the tape and a charge q at a point perpendicular to the center of the tape. Here x is the distance and l is the length of the tape. Making this adjustment the equations were rearranged and solved for q. It was found that using the distributed charge model more charges had to be transferred which is logical since the overall effect of a distributed charge is less than that of the same charge concentrated to a point.
Does this make sense?

 

[haruspex]

Simon asked for an explanation of your reasoning. I added my post because I did not even understand the physical set-up, and your second post leaves me no better informed.
I am asking for a diagram or, failing that, a description, of where these tapes are in relation to each other. Is theta the angle between them, one being vertical or horizontal; or are they parallel, each at theta to the vertical? If at an angle, are they still in contact with each other? What else holds the tapes in place?

 

[Simon Bridge]

I had expected that, as a necessary part of explaining the reasoning, a careful description of the setup would be needed. Without it, I do not know what you are reasoning about.

Start from the beginning - what is the experimental setup?
Assume neither of us have ever seen the experiment before - you have to describe it to us carefully so that we can tell what you are doing without having to look.

You have two short lengths of thin plastic (the "tape")?
They are hanging vertically in some way from some support and you notice they are attracted to each other so they make an angle to the vertical?
Am I close?

Note: you would not normally use tan function to find a component of a vector.
You seem to be mixing components along the tape with components horizontal/vertical (weight, $-mg\hat\jmath$, has no horizontal component).

 

[NihalRi]

I see , my bad :)

You have two short lengths of thin plastic (the "tape")?
They are hanging vertically in some way from some support and you notice they are attracted to each other so they make an angle to the vertical?
Am I close?

Yes that's right.
We started of by cutting two 20cm pieces of tape. We stuck them to a table and quickly pealed them of which left them with what we are assuming to be the same charge. Then we moved these two pieces closer together holding them at the top end.

As these two pieces were brought closer together we noticed the electric force taking effect and stopped moving them together. At this point we took note of theta and r as shown in the picture below.

At this point we also took note of the forces acting on each piece of tape.

So the F of tension balances out both the electrostatic and gravitational force acting on the tape. We know that the vertical component of the tension force is equal to mg and used the tan function to calculate the horizontal component. Does this clear things up?

 

[Simon Bridge]

You were moving the tape trips towards each other until the electric force was just enough to hold the ends apart.
So shouldn't the electric force point the other way to your diagram?
(Also considering they have the same charge - like charges repel right?)

 

[haruspex]

Does this clear things up?

Partly. As Simon notes, if they are like charges they should be repelling, not attracting. From the diagram, it looks as though there is some opposite charging in the top halves of the tapes, and no charge in the lower halves.