A solid conducting sphere S of radius rests on an insulating stand
PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Conductors and Capacitors · Conductors and Capacitors
Problem
A solid conducting sphere S of radius r rests on an insulating stand. A negatively charged rod is slowly brought to a fixed distance d(d≫r) from the center of the sphere but never touches it. While the rod is in place, the sphere is momentarily connected to ground with a thin wire; the wire is then removed, followed by removal of the rod.
Immediately afterward, the now-charged sphere S is brought into contact with an identical neutral conducting sphere T that is also on an insulating stand. After the spheres touch, they are separated to a large distance apart.
Assume no charge is lost to the surroundings and ignore fringe effects.
(a) Using conservation of charge, determine the sign of the net charge that remains on sphere S after the grounding wire and rod have both been removed. Explain your reasoning without invoking any formulas.
(b) Qualitatively describe the spatial distribution of charge on sphere S just before it is brought into contact with sphere T, and explain why that distribution occurs.
(c) Determine the final net charge on each sphere after they are separated from contact. Provide a clear chain of reasoning linking each stage of the process.
(d) Suppose instead that the grounding step were skipped (the wire was never attached) while all other steps remained the same. Predict how the answers to parts (a) and (c) would change, if at all, and fully justify your prediction.