Two identical conducting spheres A and B are initially neutral and in contact. If 1.0×10^12 electrons are added to sphere A and the spheres are then separated, what is the charge on each sphere after separation?

• A. -1.6e-7 C
• B. -8e-8 C
• C. 0 C
• D. +1.6e-7 C

Answer: (B)

When two identical conducting spheres are connected, the charge distributes equally between them because they have the same capacitance and must reach the same potential. The electrons added to one sphere give the system a net negative charge, which is shared equally once the spheres are in contact.

Each electron carries charge -e = -1.60×10^-19 C. Adding 1.0×10^12 electrons to sphere A adds a charge of - (1.0×10^12)(1.60×10^-19 C) = -1.60×10^-7 C. Since the initial system was neutral, the total charge after addition is -1.60×10^-7 C. When the spheres touch, this total is split equally, so each sphere has (-1.60×10^-7 C)/2 = -8.0×10^-8 C.

After separation, each sphere carries about -8×10^-8 C, an excess of electrons on each sphere.