How many electrons must be removed from each of two 5.0 kg copper spheres to make the electric f

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How many electrons must be removed from each of two 5.0 kg...

How many electrons must be removed from each of two $5.0 \mathrm{kg}$ copper spheres to make the electric forces of repulsion between them equal in magnitude to the gravitational forces of attraction between them? Assume the distance between the spheres is large compared with their diameters.

Key Concepts

Charge Quantization

The principle of charge quantization asserts that charge comes in discrete quantities, typically as integer multiples of the elementary charge, e. This is significant when determining how many electrons (or units of elementary charge) must be removed or added to an object to achieve a specific net charge.

Equating Gravitational and Electrostatic Forces

In problems where the electric repulsion is set equal to the gravitational attraction, the formulas from Newton’s law of gravitation and Coulomb’s law are equated. This approach allows one to solve for the required net charge on each object, which can then be related to the number of electrons removed or added via charge quantization.

Newton's Law of Universal Gravitation

This law states that every pair of masses attracts each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It provides a mathematical description of gravity, which is essential for comparing gravitational forces with other forces such as the electrostatic force.

Coulomb's Law

Coulomb's law describes the force between two charged objects, stating that the electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This concept is crucial for understanding how electric forces compare in magnitude and behavior to gravitational forces.

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