What Is the Final Charge on Sphere C?

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SUMMARY

The final charge on Sphere C is +2q after a series of charge transfers involving three identical metal spheres: A (+5q), B (-q), and C (initially neutral). When Spheres A and B are touched together, they share their charges equally, resulting in both having a charge of +2q upon separation. Subsequently, when Sphere C touches Sphere A, it acquires a charge of +2q. Finally, touching Sphere C to Sphere B does not change its charge, as Sphere B has a negative charge that does not affect Sphere C's positive charge. The total charge on the three spheres remains constant at +4q before and after the interactions.

PREREQUISITES
  • Understanding of electrostatics and charge transfer principles.
  • Familiarity with the concept of charge conservation.
  • Knowledge of how identical conductive spheres distribute charge upon contact.
  • Basic algebra for calculating final charges after interactions.
NEXT STEPS
  • Study the principles of electrostatics, focusing on charge distribution and transfer.
  • Learn about the conservation of charge in electrostatic interactions.
  • Explore problems involving multiple conductive spheres and charge equalization.
  • Investigate the effects of different charge configurations on conductive materials.
USEFUL FOR

Students in physics, particularly those studying electrostatics, as well as educators looking for examples of charge transfer and conservation principles in conductive materials.

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Homework Statement


Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +5q. Sphere B carries a charge of -q. Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere C is then touched to Sphere A and then separated from it. Lastly, Sphere C is touched to sphere B and then separated from it. (a) How much charge ends up on sphere C? What is the total charge on the three spheres (b) before they are allowed to touched each other and (c) after they have touched.


Homework Equations





The Attempt at a Solution


I understand most concepts related to this but my teacher hasn't really explained everything about charge transfer to us yet. I just don't know how the charge cleanly transfers.

Thanks for any effort! =D
 
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Just approach the problem with the idea that when they contact, the charges equalize on the 2 spheres, ie if a -8q sphere touches a -4q then they should both end up at -6q, if they were identical spheres as the charge densities of the -8 and -4 would be identical and spread out between the two equal spheres.
 
Ahhh... that's what I did at first, but I just had to go wrong somewhere... Thanks for leading me back to that!
 

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