Find potential of a ball inside a grounded shell

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SUMMARY

The discussion centers on calculating the electric potential of a metal ball with radius r1, surrounded by a grounded conducting shell with radius r2. The potential of the ball is expressed as v_ball = kq/r1 + k(-q)/r2, where q is the induced charge on the shell due to the ball. The grounded condition of the shell ensures that its potential is zero, which is crucial for accurately determining the potential of the ball. Participants confirm that considering the potential due to the shell is necessary for the calculation.

PREREQUISITES
  • Understanding of electrostatics, specifically electric potential and charge induction.
  • Familiarity with the concepts of grounded conductors and their implications on electric fields.
  • Knowledge of the formula for electric potential, v = kq/r, where k is Coulomb's constant.
  • Basic grasp of spherical conductors and their behavior in electrostatic scenarios.
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  • Study the principles of electrostatics, focusing on grounded conductors and their effects on surrounding charges.
  • Learn about the method of images in electrostatics to simplify complex charge configurations.
  • Explore the derivation and applications of the electric potential formula in various geometries.
  • Investigate the behavior of induced charges in different configurations of conductors and insulators.
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Students and professionals in physics, particularly those specializing in electrostatics, electrical engineering, and anyone involved in theoretical or applied electrostatic problems.

tigigi
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I have this question that initially a metal ball of radius r1 with potential v1, then surrounded by a conducting shell with radius r2. Find potential of ball if shell grounded.

So v1 =kq/r1, then q=vr1/k, can I say directly that shell will have -q since it's induced by ball?
Then v ball will be kq /r1 + k(-q)/r2 ?
I'm not sure if I find should count the potential due to shell when I find the v ball?
Thanks for help.
 
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Looks correct.
tigigi said:
I'm not sure if I find should count the potential due to shell when I find the v ball?
You'll need that, or the condition that the shell has a potential of zero. Both approaches are possible and looks very similar.
 

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