How Do You Calculate the Charges on Two Spheres in Electrostatic Equilibrium?

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SUMMARY

The discussion centers on calculating the electrostatic charges on two spheres in equilibrium, where one sphere has a charge twice that of the other. The spheres, each with a mass of 50.0 mg, are suspended by massless threads of 50.0 cm length, forming an angle of 6.00 degrees. The relevant equation for this problem is Coulomb's Law, expressed as F = k ((q1)(q2))/r^2, where r is the distance between the spheres, calculated to be 27.4 cm using the law of cosines. The challenge lies in incorporating the gravitational forces alongside the electric forces to solve for the charges.

PREREQUISITES
  • Coulomb's Law for electrostatic forces
  • Basic trigonometry and the law of cosines
  • Understanding of vector forces in equilibrium
  • Knowledge of gravitational force calculations
NEXT STEPS
  • Study the application of Coulomb's Law in electrostatic problems
  • Learn about vector resolution and equilibrium of forces
  • Explore gravitational force equations and their integration with electrostatic forces
  • Investigate the concept of electric field strength and its relation to charge
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This discussion is beneficial for physics students, educators, and anyone interested in electrostatics and force equilibrium analysis.

krnaudio
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Electrostatic forces helpp!

Homework Statement


Two spheres, each having a mass of 50.0 mg, are suspended from a common point by massless threads 50.0 cm long. One of the spheres have been given a charge twice that of the other. The strings make an angle of 6.00 degrees.
What are the charges on each of the spheres?


Homework Equations


F = k ((q1)(q2))/r^2


The Attempt at a Solution



Since the lengths of the strings on both sides are 50 cm, I drew an imaginary line between the two spheres. I found out that the other two angles had to be 87 degrees because both of the sides were equal. Then, I used law of cosines to find that the length between the spheres is 27.4 cm, which would be r in the equation. I also know that either q1 = 2q2 or q2 = 2q1, but I do not understand how I am supposed to use the masses of the spheres to find out the charge. Is there an equation that I'm missing here??
 
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krnaudio said:

Homework Statement


Two spheres, each having a mass of 50.0 mg, are suspended from a common point by massless threads 50.0 cm long. One of the spheres have been given a charge twice that of the other. The strings make an angle of 6.00 degrees.
What are the charges on each of the spheres?

Hi krnaudio ! Welcome to PF! :smile:

There are three forces on each sphere … tension, gravity, and electric …

so make the vector sum zero (or draw a vector triangle ) :wink:
 

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