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Electric force refers to the attractive or repulsive interaction between any two charged objects. This concept is fundamental to understanding Coulomb's Law, which describes how the force depends on the magnitudes of the charges and the distance between them.
The electric force is mathematically represented by the formula \( F = k \frac{|q_1 q_2|}{r^2} \), where:

• \( F \) is the force between the charges.
• \( k \) is Coulomb's constant \((8.99 \times 10^9 \text{ N m²/C²})\).
• \( q_1 \) and \( q_2 \) are the magnitudes of the charges.
• \( r \) is the distance separating the charges.

In this exercise, we analyze how electric forces are responsible for the interactions between two point charges. They push each other with a repulsive force, as both charges are negative.
This repulsive nature arises because like charges repel, opposing each other with a calculated force through the principles of electric force.

Point charges refer to the idealized representation of charged objects in physics. This concept assumes charges to be concentrated at a single point in space, simplifying the calculation of electric forces.
Point charges are crucial in applying Coulomb's Law effectively since it helps to focus on calculating the impact of charges without considering the physical size and shape. In this exercise, the charges are negatively charged point charges separated by 10 cm. By treating these as point charges, we can easily compute the forces acting on them using Coulomb’s formula. This allows us to concentrate solely on the interactions caused by the charges themselves, shedding complexities tied to real-world dimensions and charge distributions.

Charge distribution plays a critical role in determining electric forces. It denotes how electric charge is spread across a given object or system. In problems involving point charges, charge distribution can influence the net forces experienced by the charges.
In our exercise, each charge was considered as a point with a specific numerical value, and the relationship was established such that one charge is three times the other. This uneven charge distribution influences both the initial and subsequent interactions between the charges. When charges are uniformly distributed, as in the alternate scenario where the total charge is equally split between two charges, it alters the force calculated by Coulomb's Law. This demonstrated that proper knowledge of charge distribution affects the outcome regarding how forces interact and manifest between various charges in a given environment.

Repulsive force arises between two like charges, meaning elements that have similar kinds of electric charge, such as two positive or two negative charges. In this particular exercise, the repulsive force is of primary interest because both charges involved are negative. Since like charges experience a repulsive interaction, it causes the charges to move apart from each other.
The strength of this repulsive force depends on the amount of charge each point charge holds and their separation distance. Using Coulomb's Law, this interaction is quantified to show how two negative charges repel each other with a force specified in micro-Newtons. Repulsive force has real-world implications, influencing how charge-based systems behave, from atomic particles to larger scale electrical applications, underscoring the practical importance of understanding these fundamental principles.