Two conducting spheres are initially neutral and connected by a thin conducting wire
PHYSICS · Single correct · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential
Problem
Two conducting spheres are initially neutral and connected by a thin conducting wire. The smaller sphere has radius 3cm and the larger sphere has radius 6cm. A positively charged plastic rod is brought near the smaller sphere without touching it. While the rod is present, the wire is disconnected. After the rod is removed, which sphere carries the greater magnitude of charge, and why?
(a) The smaller sphere, because charges accumulate more at surfaces with greater curvature.
(b) Both spheres carry equal-magnitude charges since the total charge of the two-sphere system remains zero.
(c) The larger sphere, because while they were connected the spheres had to be at the same potential, which requires a charge proportional to radius; therefore the sphere of radius 6cm retains the greater charge.
(d) The larger sphere, because the charge spreads out so that the surface charge density is the same everywhere, giving the bigger sphere more total charge.