Force on charges separated by grounded spherical condcutor

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SUMMARY

The discussion centers on calculating the force between two charges positioned outside a grounded conductive spherical shell. The initial assumption that the force can be calculated using the formula F=(q^2)/(4d^2) is incorrect due to the influence of the conductive sphere. The presence of the sphere causes charge redistribution, leading to additional electrostatic effects that must be considered, specifically at distances of d-R and d+R. The correct approach involves recognizing these effects to derive the accurate force expression.

PREREQUISITES
  • Understanding of electrostatics, particularly Coulomb's Law
  • Knowledge of grounded conductive spherical shells and their properties
  • Familiarity with charge distribution and induced charges
  • Basic principles of dimensional analysis in physics
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  • Study the effects of grounded conductors on nearby charges
  • Learn about electrostatic shielding and its applications
  • Explore the method of images in electrostatics
  • Review dimensional consistency in physical equations
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Students and professionals in physics, particularly those studying electrostatics, electrical engineering, and anyone involved in problems related to charge interactions and conductive materials.

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Homework Statement


Grounded conductive spherical shell is given. Radius R. Charge is held in d and (-d).
d>R. as in the pic.
What is the force on the right charge?

Homework Equations


F=q*q/r^2


The Attempt at a Solution


I thought it's just F=(q^2)/(4d^2).
Why it's wrong?
the right answer is marked.
Tnx.
 

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Your suggestion would be correct if there were no conductive sphere there. However, the sphere has some effects. The presence of the positive charge to the right will electrostatically pull some negative charge to the rightmost surface of the sphere, and similarly on the leftmost surface of the sphere (except opposite polarity). That is the source of the extra terms at a distance of d-R and d+R respectively.

That said, I am unsure about the final expression, it doesn't quite seem dimensionally consistent but it is the only answer which seems to have charges in the right spots with the right polarities.
 

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