If two identical conducting spheres are in contact, any...

If two identical conducting spheres are in contact, any excess charge will be evenly distributed between the two. Three identical metal spheres are labeled $A, B,$ and $C .$ Initially, $A$ has charge $q, \mathrm{B}$ has charge $-q / 2,$ and $\mathrm{C}$ is uncharged. What is the final charge on each sphere if $\mathrm{C}$ is touched to $\mathrm{B},$ removed, and then touched to A?

Key Concepts

Electrostatic Equilibrium

Electrostatic equilibrium is the state in which a conductor’s charges are at rest, and there is no net movement of charge within it. When conductors are brought into contact, they exchange charges until they reach the same electric potential, leading to a state of electrostatic equilibrium. This concept is crucial in understanding how charges settle on conductors after they interact.

Conservation of Charge

The law of conservation of charge states that the total electric charge in an isolated system remains constant over time, regardless of any interactions that occur between objects. This fundamental principle ensures that during the redistribution of charge between connected conductors, the sum of all charges before and after contact remains unchanged.

Charge Distribution

Charge distribution refers to the way electric charge is spread out over the surface or within a material. When identical conductors come in contact, the total charge gets equally divided between them. This principle holds true regardless of the signs or initial amounts of charge, leading to an averaged charge state that satisfies the conditions of uniform potential across the conductors.

Conductors

Conductors are materials in which electric charge can move freely. In electrostatic problems, conducting spheres are often used because when they are brought into contact, the free charge redistributes uniformly over their surfaces. This makes them ideal for studying principles like charge distribution and equilibrium.

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