Electric Potential of Two Spheres

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SUMMARY

The discussion centers on the electric potential of two insulated spherical conductors, where the first sphere of radius r1 carries a charge Q and the second sphere of radius r2 is initially uncharged. Upon connecting the two spheres with a long conducting wire, the electric potential of both spheres equalizes due to their conductive nature, resulting in the equation kQ1/r1 = kQ2/r2. The total charge is conserved, leading to the relationship Q = Q1 + Q2, where Q1 and Q2 represent the charges on the first and second spheres, respectively.

PREREQUISITES
  • Understanding of electric potential and charge distribution
  • Familiarity with the concept of conductors and their properties
  • Knowledge of Coulomb's law and the constant k (Coulomb's constant)
  • Basic principles of electrostatics and electric fields
NEXT STEPS
  • Study the derivation of electric potential for spherical conductors
  • Explore the concept of charge conservation in electrostatics
  • Learn about the behavior of electric fields around conductors
  • Investigate the implications of connecting multiple conductive objects
USEFUL FOR

Students of physics, electrical engineers, and anyone interested in understanding electrostatics and the behavior of conductive materials in electric fields.

boderam
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Problem:

An insulated spherical conductor of radius r1 carries a charge Q. A second conducting sphere of radius r2 and initially uncharged is then connected to the first by a long conducting wire. After the connection, what can you say about the electric potential of each sphere? How much charge is transferred to the second sphere? Assume the connected spheres are far apart compared to their radii. (Why make this assumption?)


I think I am confused about potential in general, so bare with me here. I know that for a point charge Q the potential at a point P is kQ/r. In class my teacher derived the potential for a sphere, in the case of the first sphere it would be kQ/r. The charge then distributes to the other sphere, but I am not sure how to derive the balance. I also know that the potential will be the same on both spheres since they are conducting, the electric field is 0. Let the first sphere have charge Q1 and the second Q2, then Q = Q1 + Q2. V = kQ1/r = kQ2/r since the potentials are equal...I don't think is right though. Someone want to clear this up for me? Thanks. A lot.
 
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anyone know how to do this?
 
Yeah that's right, the potential of each sphere is equal after they're connected, so kQ1/r1=kQ2/r2.
 

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