Electrostatic force including coulombs law

AI Thread Summary
The discussion revolves around calculating the electrostatic force between two charged spheres, where a portion q of charge Q is transferred to a second sphere. The equation used is F = k(Q-q)q/r^2, and the goal is to find the value of q/Q greater than 0.5 that results in the force being half of its maximum value. The user differentiates the force equation but seeks clarification on how to set the derivative equal to 1/2 of the maximum force to solve for the q/Q ratio. The challenge lies in determining the appropriate values to substitute for Q and r, which are treated as constants in the analysis. The discussion emphasizes the need for a clear approach to solving the problem mathematically.
th3plan
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Homework Statement



Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q/Q>0.5 will the electrostatic force between the two parts have 1/2 of the maximum possible value?



The Attempt at a Solution



ok i drew a picture and i know that sphere 1 is Q-q , and sphere 2 is q, and i plug into equation

F=k(Q-q)q/r^2

i differentiate and get qQ-2q now what i do from here, to get 1/2 maximum possible value

i know to get maximum i set equal to zero, do i set this equal to 1/2? How would i solve it for q/Q ratio if its equal to 1/2?
 
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Q is a constant. just set it equal to 1. same with r.
 

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