Understanding Electrostatic Forces: When Two Unlike Charges at 1 Meter Distance Experience 0.108 Newtons of Mutual Attraction

When delving into the fundamental principles of electrostatics, one intriguing concept is the mutual attraction or repulsion that charges exert upon each other. This phenomenon is governed by Coulomb's law, which describes the force between two point charges with respect to their distance and the magnitudes of the charges themselves.

The Basics of Coulomb's Law

Coulomb's law states that the force ((F)) between two point charges ((q_1) and (q_2)) is directly proportional to the product of the charges and inversely proportional to the square of the distance ((r)) between them. Mathematically, this is expressed as:

(F k_e frac{q_1 q_2}{r^2}), where

(k_e) is Coulomb's constant, approximately equal to (8.99 times 10^9 , frac{N cdot m^2}{C^2}). (q_1) and (q_2) are the magnitudes of the charges in coulombs (C). (r) is the distance between the charges in meters (m). (F) is the force between the charges in newtons (N).

Evaluating the Given Scenario

In the provided scenario, we have two unlike charges (meaning one is positive and the other is negative) placed 1 meter apart, exerting a mutual attractive force of 0.108 Newtons. To evaluate the magnitudes of the charges, we can use Coulomb's law. Let's denote the charges as (q_1) and (q_2), with (q_2 3q_1), as the charges are in the ratio of 1:3.

Substituting into Coulomb's law:

(0.108 8.99 times 10^9 times frac{(q_1)(3q_1)}{1^2})

This simplifies to:

(0.108 26.97 times 10^9 , q_1^2)

Solving for (q_1):

(q_1^2 frac{0.108}{26.97 times 10^9})

(q_1^2 4 times 10^{-13})

(q_1 sqrt{4 times 10^{-13}} 2 times 10^{-6}, C)

Therefore, (q_1 2 times 10^{-6}, C), and (q_2 3 times 2 times 10^{-6} 6 times 10^{-6}, C). So, we now know the magnitude of the charges involved.

Finding the Forces with Different Charge Ratios

The question further asks if this force remains the same with a different charge ratio of 1:3. Upon closer examination, it's crucial to note that the force at given conditions (1 meter apart, 0.108 Newtons) is specific to the chosen charges. If we alter the charge ratio, the force will change as well, unless the product of the charges remains constant.

Let's consider another case where the charges are in the ratio of 1:3 but with different magnitudes. If we take the original charges to be (2 times 10^{-6}, C) and (6 times 10^{-6}, C), any change in their ratio (while maintaining the product constant) would necessitate a different force due to the direct proportionality of the force to the product of the charges' magnitudes.

Conclusion: Electrostatic Forces and Charge Ratios

Electrostatic forces, represented by Coulomb's law, are influenced by the distance between charges and the magnitudes of the charges themselves. The given scenario with a force of 0.108 Newtons at a 1-meter distance for charges in a 1:3 ratio provides specific insight into these principles. When altering the charge ratio, the force will change, unless the product of the charges remains constant.

Understanding these principles is essential for various applications, from the design of electrical circuits to the behavior of particles at a microscale. The key takeaway is that while ratios of charges can be manipulated, the force's magnitude is dependent on both the charge magnitudes and their separation distance.

Keywords: Electrostatic force, Coulomb's law, charge ratio

Tags: physics, electrostatics, electrical engineering, scientific principles