Metal sphere A of radius 12.0 cm carries 6.00 μC of charge, and metal sphere B of radius 18.0

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Metal sphere A of radius 12.0 cm carries 6.00 μC of charge,...

Metal sphere $A$ of radius $12.0 \mathrm{~cm}$ carries $6.00 \mu \mathrm{C}$ of charge, and metal sphere $\mathrm{B}$ of radius $18.0 \mathrm{~cm}$ carries $-4.00 \mu \mathrm{C}$ of charge. If the two spheres are attached by a very long conducting thread, what is the final distribution of charge on the two spheres?

Key Concepts

Charge Redistribution in Connected Conductors

In systems where conductors are connected by a conducting path, charges move in such a way that the potential at every point becomes equal. This redistribution process is governed by factors such as the geometry of the conductors and the relationship between charge and potential, leading to a proportional distribution based on properties like the radii in the case of spherical conductors.

Conservation of Charge

The law of conservation of charge states that the total charge in a closed system remains constant over time. When charges are redistributed between connected conductors, the sum of the charges before and after the redistribution must be equal, ensuring that no charge is lost or gained during the process.

Equipotential Principle

When conductive objects are connected together, the charges redistribute until all parts of the conductor reach the same electric potential. This principle means that, regardless of the differences in shape or size, the entire conducting system will share a common potential in equilibrium.

Electric Potential of a Spherical Conductor

For a conducting sphere, the electric potential is directly related to the amount of charge on it and inversely related to its radius, typically expressed by the formula V = kQ/R, where k is Coulomb's constant. This relation explains why spheres of different sizes will acquire different amounts of charge when they come to the same potential.

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