How Far is Charge C from Charge A When the Force on It Is Zero?

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SUMMARY

In this discussion, participants analyze the problem of determining the position of charge C between charge A (+2.00 C) and charge B (+3.00 C), which are 3.00 m apart, such that the net force on charge C is zero. The key equation used is Coulomb's Law, F = k * Q1 * Q2 / r^2, where the forces exerted by charges A and B on charge C must be equal. The relationship between the distances from charge C to charges A and B is established as R1 + R2 = 3.00 m, allowing for the formulation of a solvable equation. Ultimately, the solution requires setting the forces equal and solving for the unknown distance R1.

PREREQUISITES
  • Coulomb's Law
  • Understanding of electric charge and forces
  • Basic algebra for solving equations
  • Concept of net force in electrostatics
NEXT STEPS
  • Practice solving problems involving Coulomb's Law with multiple charges
  • Explore the concept of electric field and its relation to force
  • Learn about the superposition principle in electrostatics
  • Investigate numerical methods for solving binomial equations
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This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those preparing for exams involving electric forces and charge interactions.

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Homework Statement


Charge A and charge B are 3.00 m apart, and charge A is +2.00 C and charge B is +3.00 C. Charge C is located between them at a certain point and the force on charge C is zero. How far from charge A is charge C?


Homework Equations





The Attempt at a Solution


I am reviewing for my final and I can't remember how to do this! I wanted to use...
F = K*Q1*Q2 / r^2
But I can't have 0 in the denominator so I know I am missing something obvious...but I am not seeing it.
 
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you're solving for when the NET force is zero. let A be charge of A, B be charge of B, and C for C, etc. distance d apart. so the distance from C to A is R1, and C to B is R2 then R1 + R2 = d.
and the 2 forces need to equal each other - i.e. F1 = kAC/(R1^2) = kBC/(R2^2) does that make sense?
 
Well yea but I don't have R2? So I tried using like R2 = 3- R1 but I can't get that to work...
 
thats how you have to do it, R1 and R2 are linked by the constant d (3 in this case). you'll end up with a binomial or something that you can solve numerically if nothing else.
A/(R1^2) = B/(3-R1)^2
 

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