Electric Charge given two forces and distance

AI Thread Summary
The discussion revolves around calculating the initial charges on two identical, positively charged conducting spheres that repel each other with a known electrostatic force. Initially, the force between the spheres is F1 = 0.0615 N when they are 38.2 cm apart. After connecting them with a wire, the force increases to F2 = 0.100 N due to charge redistribution. The user attempts to apply Coulomb's Law but encounters a problem where the charges cancel out, leading to confusion. The conversation seeks guidance on how to correctly approach the problem to find the initial charges, q1 and q2, given the conditions.
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Homework Statement



There are two identical, positively charged conducting spheres fixed in space. The spheres are 38.2 cm apart (center to center) and repel each other with an electrostatic force of F1= 0.0615N. Then, a thin conduction wire connects the spheres, redistributing the charge on each sphere. When the wire is removed the spheres still repel but with a force of F2=0.100N. Using this information, find the initial charge on each sphere, q1 and q2 if initially q1<q2. The Coulomb Force constant is k= 8.99*10^9 N*m^2/C^2

Hint: Assume the spheres are in a one-dimensional plane to simplify the calculation.

Homework Equations



Coulombs Law: F=(k*q1*q1)/r^2

The Attempt at a Solution



I set up coulombs law equation and solved for q1, then plugged it back into the equation, but all the charges canceled out
 
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and I was left with F1=F2, which isn't true in this scenario. I'm stuck and have no idea what to do. Any insight would be greatly appreciated!
 
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