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

AI Thread Summary
To calculate the charges on two spheres in electrostatic equilibrium, consider the forces acting on each sphere: tension, gravity, and electric force. The spheres have equal masses of 50.0 mg and are suspended by threads at a 6.00-degree angle. One sphere has a charge that is twice that of the other, leading to a relationship between the charges. The distance between the spheres can be determined using the law of cosines, and the electrostatic force equation F = k ((q1)(q2))/r^2 can be applied to find the charges. Understanding the balance of forces is crucial for solving the problem.
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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