Calculating Charge in Equilibrium for an Electrostatics Problem

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To find the charge q_1 in static equilibrium with q_2, the forces acting on a central particle with a charge of -3.0 nC must be equal and opposite. The formula F = |q1||q2|*K/(r^2) is applied, assuming q_1 equals q_2. By setting the forces equal, the equation k*Q2*Q3/d^2 = k*Q2*Q1/(2d)^2 is derived. Solving this leads to the conclusion that q_1 must be 12 nC. The discussion emphasizes the importance of understanding the balance of forces in electrostatic equilibrium.
Linus Pauling
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1. q_2 is in static equilibrium. What is q_1?

There's a particle with a charge of -3.0nC between q_1 and q_2, 10cm from each.



2. F = |q1||q2|*K/(r^2)


3. I know the answer is 12 nC but I don't see how to get it. I figured you had to approach the problem using the above equation, knowing that q1 must equal q2 and the forces each exerts on the central particle are equal in magnitude and opposite in sign...
 
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Assume Q2 fixed.
For equilibrium,
k*Q2*Q3/d^2 = k*Q2*Q1/(2d)^2.
Now solve for Q1.
 

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