Finding Equilibrium Position for Third Charge in Line of Point Charges

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SUMMARY

The discussion focuses on determining the equilibrium position for a third charge, q3, placed along the x-axis between two existing point charges: +8.4 µC at the origin and -3.8 µC at x = 10.0 cm. The key equation used is Coulomb's Law, F=(kq1 q2)/r^2, which describes the force between point charges. The challenge arises from the lack of specific information regarding the magnitude of q3, leading to difficulties in solving for its position. The solution requires setting the net force on q3 to zero, which can be achieved by equating the forces exerted by the two existing charges.

PREREQUISITES
  • Coulomb's Law for electrostatic forces
  • Understanding of equilibrium conditions in physics
  • Basic algebra for solving equations
  • Concept of point charges and their interactions
NEXT STEPS
  • Study the concept of electrostatic equilibrium in detail
  • Learn how to apply Coulomb's Law to multiple point charges
  • Explore the effects of varying charge magnitudes on equilibrium positions
  • Investigate graphical methods for visualizing forces between charges
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone studying electrostatics, particularly those interested in the dynamics of point charges and equilibrium analysis.

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Homework Statement


Two point charges lie on the x axis. A charge of +8.4 µC is at the origin, and a charge of -3.8 µC is at x = 10.0 cm.
At what position x would a third charge q3 be in equilibrium?


Homework Equations


F=(kq1 q2)/r^2


The Attempt at a Solution


I think that my main problem was that I wasn't quite sure how to solve for the distance if I don't have the charge for the third particle or its relation to the other charges.
 
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Then, simply use q3 as the value each time you plug it into your relevant equation. It should cancel out later.
 
I tried that, but the q3 doesn't cancel out and I don't know how to get rid of it because they don't state any relationships between the charges. (ex: q1=q, q2=-3q, etc.)
 

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