Two identical small metal spheres initially carry charges q1...

Two identical small metal spheres initially carry charges $q_{1}$ and $q_{2}$. When they're $1.0 \mathrm{~m}$ apart, they experience a $2.5-\mathrm{N}$ attractive force. Then they're brought together so charge moves from one to the other until they have the same net charge. They're again placed $1.0 \mathrm{~m}$ apart, and now they repel with a $2.5-\mathrm{N}$ force. What were the original charges $q_{1}$ and $q_{2}$ ?

Two identical small metal spheres initially carry charges $q_{1}$ and $q_{2}$. When they're $1.0 \mathrm{~m}$ apart, they experience a $2.5-\mathrm{N}$ attractive force. Then they're brought together so charge moves from one to the other until they have the same net charge. They're again placed $1.0 \mathrm{~m}$ apart, and now they repel with a $2.5-\mathrm{N}$ force.
What were the original charges $q_{1}$ and $q_{2}$ ?

Key Concepts

Coulomb's Law

Coulomb's Law quantifies the electrostatic force between two point charges by stating that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This principle is fundamental in analyzing interactions between charged objects, whether they repel or attract each other.

Charge Redistribution in Identical Conductors

When two identical conductors are brought into contact, they redistribute charge to equalize their electric potential. This means that the total charge is shared equally between them. Understanding this concept is key when dealing with scenarios where charge is transferred or shared, as it can change the nature of the forces experienced between the conductors.

Sign of Charges and Nature of Electrostatic Forces

The sign of the charges involved determines whether the electrostatic force is attractive or repulsive. Opposite charges attract each other, while like charges repel each other. Recognizing this relationship is essential when analyzing situations where the direction of the force gives clues about the charges’ signs and magnitudes.

Conservation of Charge

The principle of conservation of charge states that the total electric charge in an isolated system remains constant over time. This concept is crucial when charges are transferred between objects or redistributed, as the sum of the individual charges before and after any process remains unchanged.

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