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Coulomb's Law is one of the foundational principles in electrostatics, describing how charged objects interact. It provides the formula to calculate the electrostatic force between two stationary point charges. The electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This relationship is expressed as:\[F = \frac{k \cdot |q_1 \cdot q_2|}{r^2}\]Here, \(k\) is known as Coulomb's constant and has a very large value of approximately \(8.99 \times 10^9 \text{ N m}^2/\text{C}^2\). This constant emphasizes the strength of the electrostatic force.
Coulomb’s Law is a key concept because it allows us to quantify the electric force between two charges. This force is not just a function of the magnitude of the charges, but also how far apart they are. When applying Coulomb's Law, it's crucial to consider the sign and magnitude of the charges:

• If both charges are like (both positive or both negative), they'll repel each other.
• If they have opposite signs, they'll attract each other.

Understanding this law helps explain a vast array of phenomena, from why electrons orbit atomic nuclei to how electricity flows through wires.

The electrostatic force, also known as Coulombic force, is a fundamental interaction between electrically charged objects. In the context of the two charged particles in the exercise, the electrostatic force is a repulsive force acting along the line joining the charges. This force arises due to the natural tendency of like charges to repel each other.Calculation of the electrostatic force involves using the values provided for the charges and the distance between them, applying Coulomb's Law. In this exercise, both particles have the same charge, \(q = 2.0 \times 10^{-8} \text{ C}\), and are 1 meter apart. Plugging these into the law, we calculate:\[F = \frac{(8.99 \times 10^9) \times (2.0 \times 10^{-8})^2}{1^2} = 3.596 \times 10^{-6} \text{ N}\]This force is mutual, meaning both particles exert this force on each other equally and in opposite directions, per Newton's third law. The magnitude of this force directly determines the tension in the string tying the charges, explaining their equilibrium in the scenario provided.

In physics, tension refers to the force exerted by a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In the scenario of the two charged particles on the table, the tension in the string is a direct result of the electrostatic force of repulsion between the charges.Since electrostatic forces are mutual and equal, the tension in the string must balance this force to maintain equilibrium. This is essential since there are no other forces acting on the system due to the smooth horizontal surface. Therefore, the tension equals the electrostatic force calculated using Coulomb's Law, which is \(3.596 \times 10^{-6} \text{ N}\).Understanding the concept of tension not only applies to electrostatics but also extends to various physical systems and engineering applications.
For students, appreciating how tension synchronizes with forces like frictionless tables and electrostatic forces is crucial for analyzing and solving physics problems.