How to Find the Electric Force Between Two Charged Spheres?

AI Thread Summary
To find the electric force between two charged spheres, the setup involves two spheres with mass 14.3 kg, suspended by silk threads at an angle of 22 degrees from the vertical. The forces acting on one sphere include gravitational force, tension from the thread, and the electric force due to repulsion between the charges. The tension must be resolved into vertical and horizontal components to balance the forces correctly. The calculations for charge, using the equation Fe = k |q1||q2| / r², led to confusion regarding the distance between spheres, which was determined using trigonometric functions. Correctly resolving the tension components and accurately calculating the distance are crucial for finding the correct charge value.
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Homework Statement



Two small spheres with mass m = 14.3 are hung by silk threads of length L = 1.26 from a common point. When the spheres are given equal charges, so that , each thread hangs at an angle \theta = 22.0 from the vertical.

A. Draw a diagram showing forces on the left sphere.
B. Find the magnitude of q.

Homework Equations



Fe = k |q1||q2| / r2

The Attempt at a Solution



Part A.
I drew three forces on the left sphere. I have the force of gravity, pointing straight down from the shpere. The tension force point along the length of the thread, away from the shpere. And the Electron force pointing directly to the left. I drew the Fe pointing away because I figured both spheres have the same charge since they are being repelled apart. This answer is wrong but I am not sure why.

Part B.
I used the sum of forces.

Fx = Tx - mg = 0
Tx = mg = 0.140

Fy = Ty - Fe = 0
Ty = Fe

I calculated Ty = 1.17
Using that I found q

1.17 = kq2 / (0.944)2
q = 1.08 * 10-5

This was also wrong.

Any help will be appreciated. Thank You.
 
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Split the tension into its vertical and horizontal components.

Ty-mg=0 ! not Tx

Just remember how to split the tension,T, into its vertical and horizontal components.

also how did you get 0.994 as the distance between the spheres?
 
Sorry about that. I meant Ty but it got lost in translation from paper to computer.

I found r by using 1.26 * sin(22) = .0472. That was half the distance to one sphere so I mutliplied by 2.
 
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