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Electrostatic force is the force that occurs between two electrically charged objects. It is described by Coulomb's Law, which states that the magnitude of the force between two point 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 for this force is: \[ F = k \frac{|q_1 q_2|}{r^2} \] where:

• \(F\) is the electrostatic force,
• \(k\) is the electrostatic constant \(8.99 \times 10^9 \ N \cdot m^2/C^2\),
• \(q_1\) and \(q_2\) are the point charges,
• \(r\) is the distance between the charges.

This force can be attractive or repulsive depending on the nature of the charges involved. If the charges are of opposite signs, the force is attractive; if they are of the same sign, the force is repulsive. Understanding and calculating this force allows us to comprehend how charged particles interact in a static electric field.

Point charges refer to objects that have a very small size compared to their separation distance, allowing their charge to be treated as if it were concentrated at a single point. This simplification is essential when applying Coulomb's Law.
Point charges are fundamental in electrostatics because they create electric fields and interact via electrostatic forces. Two point charges can influence each other even when they are not in direct contact.
In the exercise, each of the charges—\(q_1 = -1.50\) nC, \(q_2 = +3.20\) nC, and \(q_3 = +5.00\) nC—is treated as a point charge. Their positions on the y-axis simplify calculations to one dimension, making it easier to apply the principle of superposition to find vector sums and net forces.

The concept of a vector sum is essential when dealing with forces in physics. Forces are vector quantities, meaning they have both magnitude and direction.
When multiple forces act on an object, the net force is determined by finding the vector sum of these individual forces. In the case of electrostatic forces between point charges, the vector sum accounts for the directionality of each force involved. This is important because different forces may not act in the same direction.
In the provided exercise, calculating the net force on charge \(q_3\) involves the vector sum of forces \(F_{31}\) and \(F_{32}\). Since these forces are along the same line but in opposite directions, their net effect is calculated by taking the difference, acknowledging that force direction is crucial to understanding resultant impacts on charge trajectories.

Electric charge interaction is the basis for explaining how charged objects exert forces upon each other. This interaction is insightful when analyzing the behavior of like and unlike charges in close proximity.
In the exercise, the interactions manifest as forces exerted by two point charges on a third charge. Here's how they interact:

• Charge \(q_1 = -1.50\) nC repels \(q_3 = +5.00\) nC because opposite charges attract, creating a force \(F_{31}\) upwards on the y-axis.
• Charge \(q_2 = +3.20\) nC attracts \(q_3\), resulting in a force \(F_{32}\) downwards, due to the like charge interaction being repulsive for other potential configurations.

This exercise helps visualize charge interaction principles, providing insights into the intricacies of electrostatic force calculations and their real-world implications. Understanding this concept is crucial for anyone studying electric fields and charges.