How to Find the Electric Force Between Two Charged Spheres?

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SUMMARY

The discussion centers on calculating the electric force between two charged spheres, each with a mass of 14.3 grams and suspended by silk threads of length 1.26 meters, forming an angle of 22.0 degrees with the vertical. The electric force equation used is Fe = k |q1||q2| / r², where k is Coulomb's constant. The user initially miscalculated the tension and electric force components, leading to an incorrect charge value of q = 1.08 x 10-5 C. Correcting the tension components and accurately determining the distance between the spheres is crucial for solving the problem.

PREREQUISITES
  • Understanding of Coulomb's Law and electric force calculations
  • Knowledge of vector components and tension in physics
  • Familiarity with trigonometric functions, specifically sine and cosine
  • Ability to manipulate algebraic equations for solving for unknowns
NEXT STEPS
  • Review Coulomb's Law and its applications in electrostatics
  • Study vector decomposition, particularly in tension and force analysis
  • Learn how to calculate distances between charged objects using trigonometric principles
  • Practice solving similar physics problems involving electric forces and angles
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Students studying physics, particularly those focusing on electrostatics and force analysis, as well as educators looking for problem-solving strategies in electric force calculations.

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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 [tex]\theta[/tex] = 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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