Electric Force And Distance How Force Changes With Tripled Distance

The electric force, a fundamental force of nature, governs the interactions between charged particles. It's the force responsible for holding atoms together, enabling chemical reactions, and powering the devices we use every day. Understanding how this force behaves is crucial in various fields, from physics and chemistry to electrical engineering and materials science. One of the key aspects of the electric force is its dependence on the distance between charged particles. This article delves into the relationship between electric force and distance, exploring how the force changes when the distance between two charged particles is altered. Specifically, we will address the question of what happens to the electric force when the distance between two charged particles is increased by a factor of 3.

At the heart of understanding electric force lies Coulomb's Law, a cornerstone of electrostatics. This law, formulated by French physicist Charles-Augustin de Coulomb in the 18th century, quantifies the electric force between two stationary charged particles. Coulomb's Law states that the electric 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. Mathematically, this law is expressed as:

F = k * (|q1 * q2|) / r^2

Where:

• F represents the magnitude of the electric force.
• k is Coulomb's constant, approximately 8.9875 × 10^9 N⋅m^2/C2.
• q1 and q2 are the magnitudes of the charges of the two particles.
• r is the distance between the centers of the two charges.

The significance of Coulomb's Law is profound. It provides a precise mathematical description of how electric force operates, allowing us to predict and calculate the force between charged objects. The law highlights two key relationships:

1. Direct Proportionality to Charge: The electric force is directly proportional to the product of the charges. This means that if you increase the magnitude of either charge, the electric force will increase proportionally. For instance, if you double the magnitude of one charge, the electric force will also double.
2. Inverse Square Law with Distance: The electric force is inversely proportional to the square of the distance between the charges. This is a crucial aspect of the law. It implies that as the distance between the charges increases, the electric force decreases dramatically, following an inverse square relationship. This means if you double the distance, the force decreases by a factor of four (2 squared). If you triple the distance, the force decreases by a factor of nine (3 squared), and so on.

Understanding Coulomb's Law is fundamental to grasping the behavior of electric forces and how they govern interactions between charged particles. The inverse square relationship with distance is a particularly important concept that will help us address the question posed in this article.

Now, let's address the central question: How does the electric force between two charged particles change if the distance between them is increased by a factor of 3? To answer this, we will directly apply Coulomb's Law and analyze how the force is affected by the change in distance.

As we established earlier, Coulomb's Law states:

F = k * (|q1 * q2|) / r^2

Let's consider the initial scenario where the electric force is F1, the charges are q1 and q2, and the initial distance is r1. The equation for this scenario is:

F1 = k * (|q1 * q2|) / r1^2

Now, let's consider the scenario where the distance is increased by a factor of 3. This means the new distance, r2, is 3 times the original distance, r1. Therefore: r2 = 3 * r1

The electric force in this new scenario, F2, can be expressed using Coulomb's Law as:

F2 = k * (|q1 * q2|) / r2^2

Since r2 = 3 * r1, we can substitute this into the equation for F2:

F2 = k * (|q1 * q2|) / (3 * r1)^2 F2 = k * (|q1 * q2|) / (9 * r1^2)

Now, let's compare F2 with F1. We can rewrite the equation for F2 as:

F2 = (1/9) * [k * (|q1 * q2|) / r1^2]

Notice that the term inside the brackets is the same as our original electric force, F1. Therefore, we can write:

F2 = (1/9) * F1

This equation reveals the answer to our question. When the distance between the two charged particles is increased by a factor of 3, the new electric force (F2) is 1/9th of the original electric force (F1). In other words, the electric force is reduced by a factor of 9.

This result perfectly illustrates the inverse square relationship inherent in Coulomb's Law. The electric force decreases dramatically as the distance increases because the force is inversely proportional to the square of the distance. When the distance is tripled, the square of the distance becomes nine times larger, leading to a ninefold reduction in the electric force.

In summary, when the distance between two charged particles is increased by a factor of 3, the electric force between them is reduced by a factor of 9. This is a direct consequence of Coulomb's Law and the inverse square relationship between electric force and distance. Understanding this relationship is crucial for comprehending the behavior of charged particles and the forces that govern their interactions. This principle has far-reaching implications in various fields, including electronics, materials science, and our fundamental understanding of the universe.

The correct answer is C. It is reduced by a factor of 9.