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Coulomb's Law is the principle that describes how electric charges interact with each other. The law states that the electric force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, this relationship can be expressed as:\[F = k \frac{|q_1 q_2|}{r^2}\]where:

• \(F\) is the electric force between charges,
• \(k\) is the Coulomb's constant \(\approx 8.988 \times 10^9 \, \text{N m}^2/\text{C}^2\),
• \(q_1\) and \(q_2\) are the magnitudes of the charges,
• \(r\) is the distance between the charges.

This law helps us understand that charges either attract or repel each other depending on their signs. Positive charges repel each other, as seen in our exercise with charges \(q\) and \(2q\).
The force's direction depends on the nature of the charges: like charges repel, while unlike charges attract.

The Superposition Principle is a fundamental concept in physics, especially in the study of electric fields. It states that the total electric field created by multiple charges is the vector sum of the electric fields produced by each individual charge.
This means that the electric fields from each charge are independent of each other, and they can be added together using vector addition.
In the context of our problem, we have two charges, \(q\) and \(2q\), each creating an electric field along the x-axis. To find the point where the total field is zero, we need to apply superposition:

• The electric field from charge \(q\) is calculated, considering its direction and magnitude.
• The electric field from charge \(2q\) is similarly calculated.
• These fields are added vectorially to determine the resultant field at any given point along the x-axis.

By applying the principle of superposition, we can locate a position between these charges where their opposing fields cancel each other out, resulting in a net electric field of zero. This is how we find that the point is closer to \(q\) because the field due to \(2q\) must be stronger to balance the lesser charge, using its greater value and distance.

Electric charge interaction is a central theme when analyzing electric fields created by multiple charges. The interaction explains how charged particles exert forces upon each other due to their electric fields.
The strength and direction of these forces or fields depend heavily on both the magnitude and sign of the charges involved as well as their respective positions.
For the given problem:

• We have two positive charges, \(q\) and \(2q\), fixed along the x-axis.
• These charges generate electric fields that emanate outward from them, as they are like charges, they repel each other.
• The interaction of these fields varies depending on the observer's position along the x-axis.

To analyze the total interaction's effect, consider the electric fields' directions caused by each charge. On one side, closer to \(q\), the electric field from \(2q\) overtakes, neutralizing the field from \(q\), thus creating a point where the electric field reaches zero. This unique point of zero total electric field showcases the delicate balance of electric charge interaction.