A small conducting sphere A of radius initially carries a charge
PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Conductors and Capacitors · Conductors and Capacitors
Problem
A small conducting sphere A of radius R initially carries a charge +Q0. A second, larger neutral conducting sphere B of radius 2R is positioned far from sphere A. The two spheres are connected with a long, thin conducting wire so that they form a single electrical system. While the wire is still attached, a negatively charged rod is brought near sphere A (without touching) and held fixed. After electrostatic equilibrium is reached in the presence of the rod, the wire is disconnected, trapping whatever charges each sphere has at that instant. The rod is then removed, and the spheres are kept far apart.
(a) Using electrostatic reasoning, describe the direction of electron flow between the two spheres during the time the rod is present and the wire connects the spheres.
(b) Derive an expression for the final charge qA on sphere A in terms of Q0 and the radii of the spheres, showing all steps that invoke conservation of charge and the requirement that the two connected conductors were at the same electric potential before the wire was removed.
(c) Given Q0=24nC and R=1.0cm, calculate the numerical values of the final charges on spheres A and B.
(d) After the rod is removed, the centers of the spheres are placed 0.60m apart. Determine whether the force between the spheres is attractive or repulsive and calculate its magnitude.