Electrostatic force including coulombs law

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SUMMARY

The discussion focuses on calculating the electrostatic force between two charged spheres using Coulomb's Law. The force is defined by the equation F = k(Q-q)q/r², where Q is the initial charge on the first sphere, q is the charge transferred to the second sphere, and r is the distance between them. To find the value of q/Q that results in the electrostatic force being half of its maximum value, the user differentiates the force equation and seeks to set the derivative equal to zero to find the maximum force. The challenge lies in determining the ratio q/Q when the force equals 1/2 of this maximum.

PREREQUISITES
  • Coulomb's Law
  • Basic calculus (differentiation)
  • Understanding of electrostatic forces
  • Concept of charge distribution
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  • Study the derivation of Coulomb's Law in detail
  • Learn about the concept of electrostatic force maximization
  • Explore calculus applications in physics, particularly optimization problems
  • Investigate charge distribution and its effects on electrostatic interactions
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Students studying physics, particularly those focusing on electrostatics, as well as educators looking for examples of applying calculus to physical laws.

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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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