# Electrostatics of ping pong ball question

1. Jun 16, 2007

### ploppers

1. The problem statement, all variables and given/known data

A ping pong ball of mass 3*10^-4 kg is hanging from a light thread 1 m between 2 vertical parallel plates 10 cm apart. When the potential difference across the plate is 420V, the ball comes to equilibrium 1 cm from one side of the original position. What is the tension of the string, charge and electric force on the ball?

2. Relevant equations

E = V/r
F = Eq

3. The attempt at a solution

found the force in the horizontal is 2.92*10^-4 through spliting up the force of gravity. Tension force is the same as it would be going straight down so I found the angle with 1 cm and 10cm and cos the force to get the horizontal force. That would be the force the system acts on it.

F = Eq
2.92*10^-4 = Vq/r
2.92*10^-4 * r / v = q

this is where I get my problem...is the potential energy conssistant throughout the system like the force? If it is then I can get to an answer, but if it isn't, what do I do? If you can;'t understand what I wrote i apologize, I'm very confused and frusterated:grumpy:

2. Jun 16, 2007

### nrqed

No, the tension is not the same as when the ball is hanging straight down (in which case T=mg). You have to draw a FBD and solve. There is not enough details in the rest of your post to see if you did it right and I did not check your final answer.
I am not sure where you got the formula F = Vq/r but that's completely wrong. But the formula "electric Force = qE" is correct.

There is a formula V=kq/r but that's the electric potential produced by a point charge. For two infinite plates, the E field is constant and is given by the potential difference between the plates divided by the plate separation, $E = \Delta V/ d$. Use that to find E and then use that the electric force is equal to q E.

3. Jun 16, 2007

### ploppers

Would you be able to show me how to properly solve this?

4. Jun 16, 2007

### nrqed

First, can you find the value of the E field using the formula I gave you?

The second step is : can you sho wme the steps you followed to find the electric foce? (this force must be equal to the x component of the tension, right? And to find this x component, you must first find the magnitude of the tension using that the net force along y is zero. Before doing this, you need to find the angle made by the string).

So the steps for the second part are

a) find the angle

b) working in the y direction, th enet force along y is zero which should allow you to find the magnitude of th etension.

c) Then go in the x direction to find the electric force

d) finally, use electric force = q E and the E found in the first step to solve for q.

5. Jun 19, 2007

### ploppers

Thnx, I followed and ot the right answer :D Actually I used the wrong variables for my equations. My Vq/r is actually combining the F = (funky E)q with (funky E) = V/d.

However, I still wonder why I would use the 10 cm for d. is the V always the same between 2 plates? That would make no sense.....