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Two isolated spherical conducting shells carrying charges Q1 and Q2 with radii r1 and r2 are placed very far apart. They are then connected by a conducting wire. Choose the INCORRECT statement: (A) The electrostatic potential energy of the system must decrease. (B) The electrostatic potential energy of the system may decrease. (C) If Q1*r2 = Q2*r1, then no charge flows through the wire. (D) If Q1*r2 = Q2*r1, then the electrostatic potential energy of the system is already a minimum.

1. The electrostatic potential energy of the system must decrease.
2. The electrostatic potential energy of the system may decrease.
3. If Q1*r2 = Q2*r1, then no charge flows through the wire.
4. If Q1*r2 = Q2*r1, then the electrostatic potential energy of the system is already a minimum.

Correct answer: The electrostatic potential energy of the system must decrease.

Solution

Connecting the shells equalizes their potentials. If they were already at the same potential (Q1/r1 = Q2/r2, equivalently Q1*r2 = Q2*r1), no charge flows and the energy stays the same (it is already minimum for the given total charge). So the energy does NOT necessarily decrease - it 'may' decrease (B is correct), and statements C and D are correct. The claim that it 'must' decrease (A) is therefore incorrect.

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