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Coulomb's Law is a fundamental principle that describes the force between two stationary point charges. It states that the electrostatic force (F) between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The formula is given by:

• \(F = k \cdot \frac{{q1 \cdot q2}}{{r^2}}\)

Here, \(k\) is Coulomb's constant, \(q1\) and \(q2\) are the charges, and \(r\) is the distance between them.

This law helps us understand how objects charged with protons and electrons interact with each other. Positive charges repel other positive charges and attract negative charges. Similarly, negative charges repel other negative charges. The direction of the force is along the line joining the two charges. This principle can be used to determine the force experienced by each charge in an electric field.

In the context of electrostatic equilibrium, as mentioned in the exercise, all charges must balance such that the net force on each charge is zero. This means that every charge should exert an equal and opposite force on the others, resulting in no movement.

The electrostatic force is the force of attraction or repulsion between two charged objects. It is one of the four fundamental forces of nature and is described by Coulomb's Law.

• This force acts over the space separating the charges, and it relies heavily on the magnitudes of the charges involved and their separation distance.

It's crucial to note that like charges repel each other while unlike charges attract each other.

Understanding this force helps in this exercise as it dictates how the third charge needs to balance forces from both existing charges, \(+Q\) and \(+4Q\).

To be in equilibrium, the net electrostatic force experienced by each charge must be zero:

• This involves setting the sum of the forces acting on each charge equal to zero, considering their directions.
• For the third charge \(q\), this involves equating the forces exerted by the charges \(+Q\) and \(+4Q\) to ensure that the net force remains balanced.

Harnessing the characteristics of the electrostatic force allows for the strategic placement of \(q\) to achieve desired balance.

Charge distribution involves the arrangement of charges in a system and how they influence one another.

In the scenario of the exercise, we want to place the third charge such that the system reaches electrostatic equilibrium:

• The position of \(q\) needs to be adjusted relative to \(+Q\) and \(+4Q\).

It plays a crucial role in determining where to place \(q\) so that it creates a balance and ensures that forces on each charge nullify each other.

To achieve equilibrium for the three charges:

• The charge \(q\)'s distance from \(+Q\) and \(+4Q\) significantly impacts the resulting forces.
• By considering the sum of forces and their directions, the exact position and magnitude for \(q\) can be determined.

In practical terms, this step includes careful calculations to ensure the electrostatic forces among the charges lead to a stable arrangement, where no charge wants to move.