Calculating Tension in a Charged Ball Suspended in an Electric Field

[Ryoblck]

Homework Statement

A tiny, 0.60g ball carries a charge of magnitude 8.0 mircoC. It is suspended by a vertical thread in a downard 300 N/C electric field. What is the tension in the thread if the charge on the ball is (a) positive, (b) negative?

Homework Equations

Fe=QE?

The Attempt at a Solution

At first I thought the equation E=(kq)/(r^2) would be useful until I read that there was no radius. Also found that angle is not necessary. I'm completely clueless as to what equation to use. The book gives me the answer (a) 8.3 mN; (b) 3.5 mN.

 

[TSny]

Hello, Ryoblck. Welcome to PF!

Can you imagine what forces act on the ball while it is suspended? Can you visualize the direction of each force? (A diagram will be helpful). Can you calculate any of these forces? Why does the ball remain at rest?

 

[Ryoblck]

Gravity is one of the forces that always acts on the ball.

 

[TSny]

Gravity is one of the forces that always acts on the ball.

Yes. Any other forces acting on the ball?

 

[Ryoblck]

I guess the 300 N/C.

 

[TSny]

I guess the 300 N/C.

The 300 N/C is the magnitude of the electric field, which is not a force. But it is closely related to one of the forces acting on the ball. (See the equation you wrote in the "relevant equations" section of your original post.) In addition, there is still another force.

It is essential to have a clear picture of all of the forces acting on the ball.

 

[Ryoblck]

Q would be 8.0 micro coulombs. I don't exactly know what E would be.

 

[TSny]

I don't exactly know what E would be.

E is stated in the problem to be 300 N/C.

 

[Ryoblck]

Well then that means there is only gravity and Q for the forces on the ball. How would I calculate gravity in? I feel like its the wrong equation bd aide there is no variable for gravity.

 

[TSny]

Well then that means there is only gravity and Q for the forces on the ball. How would I calculate gravity in? I feel like its the wrong equation bd aide there is no variable for gravity.

The force of gravity is one of the forces. Q does not represent force, it represents electric charge. In your original post, you wrote F_e = QE. What does this represent? Also, keep in mind what you are asked to find. Is that related to any force acting on the ball?

 

[Ryoblck]

It represents the force of the electric field. This can be found by using the electric charge times the magnitude of the electric field. What I'm trying to find is the tension of the thread, making this equation invalid. Knowing this, I still don't know which equation I need to start using...

 

[ap123]

The first thing you need to do before anything else is to draw a diagram with all the forces on the ball, (as pointed out in post #2 ).
Since the ball is at rest, what is the relation between these forces?

(make sure you end up with 3 forces on the ball in your diagram)

 

[Ryoblck]

I'm drawing a free body diagram. I have the ball in the middle, gravity pointing downwards, and I guess the thread pointing upwards. I have no idea for the third force though

 

[ap123]

The third force is the electric force on the charged ball - what direction is this in?
Once you determine the direction of this force then you can work out a relation between all the forces on the ball.

 

[Ryoblck]

Would the third force be 300 N/C pointing downwards?

 

[ap123]

Yes, the force is pointing downwards in part (a).
The magnitude of the force will be qE, where E is 300N/C.

So, you have 2 forces pointing down, 1 pointing up, and the ball at rest.
What's the relation between all these forces - once you have that, you can calculate the tension in the thread.

 

[Ryoblck]

So I have the right equation? But where does gravity come in?