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Electric charge is a fundamental property of matter that determines how objects interact electrically. Objects can be positively or negatively charged, depending on whether they have an excess or deficiency of electrons. In this context, an electric charge is a measure of excess electrons present in an object.
For example, when two small spheres have identical charges, it means they either have the same number of excess electrons or the same electron deficit. These charged objects create electric fields, leading to forces of either attraction or repulsion, depending on the nature of the charges.
When working with electric charge, one must remember that it is quantized, meaning it exists in discrete amounts, specifically in multiples of the charge of a single electron:

• The charge of one electron is approximately -1.602 x 10^{-19}$ C.
• Charge conservation implies the net charge remains constant in a closed system.

The force of repulsion between two like charges is an essential concept in electromagnetism, explained by Coulomb's Law. This law states that the force between any two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
When two objects have like charges (both positive or both negative), they repel each other. This phenomenon is the force of repulsion.

• The magnitude of the force of repulsion depends on both the amount of charge on each object and how far apart the objects are.
• The direction of the force is always such that the objects push away from each other, hence the term repulsion.
• In this exercise, the measured force of repulsion helps calculate the total charge and eventually determine the number of excess electrons causing this force.

Excess electrons on an object signify that it is negatively charged. To determine the number of excess electrons on an object, you must first calculate the total electric charge and then divide that by the charge of a single electron.
This problem involves calculating the number of excess electrons on two spheres. Once you have found the total electric charge on each sphere using Coulomb's Law, divide it by the electron charge (1.602 x 10^{-19} C) to find the number of excess electrons:

• Excess electrons are the additional electrons that give a sphere its negative charge.
• In our case, each sphere needs about 2666 excess electrons to create the observed force of repulsion.
• This calculation is vital for understanding how macro-level forces like repulsion result from micro-level particles like electrons.

Coulomb's constant is a crucial component of Coulomb's Law, as it allows us to calculate the electric force between charges. The constant has a fixed value k = 8.99 x 10^9 Nm^2/C^2, which explains the strength and behavior of the force through which charged particles interact.
Coulomb's constant makes it possible to determine the force between two charges, so it is always included in such calculations. In practical terms:

• It converts the unit-less product of charges into Newtons, which is a measure of force.
• It also suggests how forces scale with distance and charge magnitude.
• By using Coulomb’s constant in the formula, this exercise seamlessly links the known force with the number of excess electrons.

Understanding Coulomb's constant helps in visualizing the direct relationship between microscopic particles and macroscopic forces in the world around us.