Two identical metal spheres A and B are connected by a metal...

Two identical metal spheres $A$ and $B$ are connected by a metal rod. Both are initially neutral. $1.0 \times 10^{12}$ electrons are added to sphere $A$, then the connecting rod is removed. Afterward, what are the charge of $A$ and the charge of $B ?$

Key Concepts

Electrostatic Equilibrium

When conductors are connected, charges redistribute themselves until the potential is uniform across the entire connected system. This principle of electrostatic equilibrium ensures that no net movement of charge occurs within the conductors, as any difference in potential would cause further redistribution of charge until uniformity is reached.

Charge Redistribution in Connected Conductors

When two conductors are connected by a conductive path, any added charge can move freely between them until both have the same electric potential. In systems involving identical conductors, the charges typically distribute equally because their identical sizes and shapes mean they have equal capacitance, leading to an even split of the total charge.

Conservation of Charge

The law of conservation of charge states that the total amount of charge in an isolated system remains constant. Even when charge is redistributed between objects, the sum of the charges on all objects retains the value that was initially present, which is a fundamental principle in solving problems involving charge distribution.

Properties of Identical Conductors

Identical conductors have the same ability to store charge (equal capacitance) and, when connected, will share charge equally if no other influences are present. This symmetry simplifies analysis in charge distribution problems because each conductor will end up with an equal fraction of the total charge present in the system.

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