Summary of Electricity: Coulomb's Law

Fundamental Questions & Answers about Coulomb's Law

Q1: What is Coulomb's Law? Coulomb's Law, formulated by Charles-Augustin de Coulomb in 1785, describes the attraction or repulsion force between two point electric charges. The intensity of this force is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance that separates them.

Q2: What is the mathematical formula that represents Coulomb's Law? The formula for Coulomb's Law is expressed as ( F = k \frac{|q_1 \cdot q_2|}{r^2} ), where ( F ) is the magnitude of the electric force between the charges, ( q_1 ) and ( q_2 ) are the magnitudes of the electric charges, ( r ) is the distance between the charges, and ( k ) is the proportionality constant of the medium (Coulomb's constant).

Q3: What is Coulomb's constant (k) and what is its value? Coulomb's constant (k) is a proportionality constant that appears in Coulomb's law and depends on the medium in which the charges are inserted. In a vacuum, its value is approximately ( 8.9875 \times 10^9 N m^2/C^2 ).

Q4: How does Coulomb's Law apply to charges of equal signs and opposite signs? For charges of equal signs, the electric force is repulsive; they move away from each other. For charges of opposite signs, the force is attractive; they attract each other.

Q5: How does the distance between the charges affect the electric force between them? The electric force is inversely proportional to the square of the distance between the charges. This means that if the distance doubles, the electric force will be reduced to a quarter of its original value.

Q6: Is Coulomb's Law valid for which types of charges? Coulomb's Law is valid for point charges, that is, those that are confined to a point or a very small region when compared to the distance that separates them.

Q7: How can Coulomb's Law be used to calculate forces in a system of more than two charges? When there are more than two charges, Coulomb's Law must be applied to calculate the resultant force on each charge individually, considering the forces of all other charges on it. The principle of superposition is used to vectorially add up all the individual forces.

Q8: Can Coulomb's Law be applied to moving charges? Coulomb's Law is generally applied to static charges or those in relative rest. In situations with moving charges, magnetic effects arise that require the use of Maxwell's equations for a complete description of electromagnetic interaction.

Q9: What is the relationship between Coulomb's Law and the electric field? Coulomb's Law can be used to calculate the magnitude of the electric field created by a point charge, which is the force per unit of test charge placed at a point in space. The relationship is given by ( E = k \frac{|q|}{r^2} ), where ( E ) is the resulting electric field.

Q10: How to solve problems involving Coulomb's Law? To solve problems involving Coulomb's Law, first identify all the charges involved and their relative positions. Then, calculate the individual forces between each pair of charges using the formula of Coulomb's Law. Finally, combine the forces (vectorially, if necessary) to obtain the resultant force on each charge.

These fundamental questions and answers offer a robust guide to understanding the essentials of Coulomb's Law and preparing to apply it in different physical contexts.

Questions & Answers by Difficulty Level

Basic Q&A

Q1: What does it mean to say that a charge is "point-like"? A charge is considered point-like when its dimensions are so small in relation to the distances involved in the problem that it can be treated as if it were concentrated at a single point.

Q2: Why is Coulomb's Law only valid for point charges? Coulomb's Law is derived for point charges because it assumes a uniform charge distribution at a point. For charge distributions of non-negligible size, it would be necessary to calculate the electric force in a more complex way, integrating the contribution of each charge element.

Q3: In what units are electric charges measured in Coulomb's Law? Electric charges are measured in Coulombs (C) in Coulomb's Law.

Explanation: We start with basic questions to ensure that you have a clear understanding of the terms and fundamental principles that will be used in more complex questions.

Intermediate Q&A

Q1: Can Coulomb's Law be used to calculate force between any two charged objects? While Coulomb's Law is accurate for point charges, it can be approximated for bodies with larger dimensions, provided the distance between them is relatively large compared to their dimensions.

Q2: How does the value of Coulomb's constant (k) influence the force between the charges? The value of k directly influences the magnitude of the electric force; the higher the value of k, the greater the force for a given pair of charges and distance.

Q3: What is the difference between the electric force and the electric field in relation to Coulomb's Law? The electric force is the interaction between two or more charges, while the electric field is a property of the space around a charge that describes how it will affect other charges.

Explanation: In this step, the questions become more challenging, exploring the applicability and related concepts of Coulomb's Law. The answers are designed to build on basic knowledge, providing more depth.

Advanced Q&A

Q1: How would you calculate the electric force on one of the charges in a system of three point charges? To calculate the electric force on one of the charges in a system of three charges, you must find the force between each pair of charges (using Coulomb's Law) and vectorially add these forces to obtain the resultant force.

Q2: Is there any condition under which the force calculated by Coulomb's Law would be zero, even with the presence of charges? Yes, if the charges are symmetrically distributed in such a way that the forces cancel each other out, the resultant force on a specific charge can be zero.

Q3: How do changes in the medium around the charges affect the Coulomb force between them? Changes in the medium can alter Coulomb's constant (k), since it is dependent on the medium. Generally in material media (non-vacuum), the force is reduced due to the presence of a factor called the dielectric constant of the medium.

Explanation: Advanced questions require a deeper understanding and the ability to apply the knowledge of Coulomb's Law in complex or less intuitive situations. The answers here incorporate a level of analysis and synthesis that goes beyond mere memorization, encouraging deep conceptual understanding.

Practical Q&A

Applied Q&A

Q1: Two small identical conductive spheres, A and B, are separated by a distance of 10cm in the air and carry charges of (5 \mu C) and (-3 \mu C), respectively. What is the interaction force between them and in which direction does it act?

Answer: To calculate the interaction force between the spheres, we use Coulomb's Law: ( F = k \frac{|q_1 \cdot q_2|}{r^2} ), where ( q_1 = 5 \mu C ) and ( q_2 = -3 \mu C ), and the distance ( r = 10cm = 0.1m ).

Converting microcoulombs to coulombs: ( 5 \mu C = 5 \times 10^{-6} C ) and ( -3 \mu C = -3 \times 10^{-6} C ).

Substituting the values in the formula, including the value of ( k ) in a vacuum (( 8.9875 \times 10^9 N m^2/C^2 )):

( F = 8.9875 \times 10^9 N m^2/C^2 \cdot \frac{|5 \times 10^{-6} C \cdot (-3 \times 10^{-6} C)|}{(0.1m)^2} )

Calculating, we have:

( F = 8.9875 \times 10^9 \cdot \frac{15 \times 10^{-12}}{0.01} ) ( F = 8.9875 \times 10^9 \cdot 1.5 \times 10^{-9} ) ( F = 13.48125 \times 10^0 ) ( F = 13.48125 N )

The resultant force is repulsive, because the charges have opposite signs. Therefore, the force acts in the direction of pushing sphere A (positive) away from sphere B (negative).

Experimental Q&A

Q1: How would you design a simple experiment to demonstrate Coulomb's Law using materials accessible in a school laboratory?

Answer: To demonstrate Coulomb's Law, you can design an experiment with slightly charged balloons and a metric line. Follow these steps:

1. Rub two balloons on a wool fabric to create static charges through triboelectricity. Make sure both balloons are electrically charged with the same type of charge (positive or negative).

2. Hang one balloon on a fixed support through a wire so that it can move freely.

3. Bring the other charged balloon close and measure the initial distance between them when you start to notice that the suspended balloon is repelled. This is the distance at which the repulsion force begins to be noticeable.

4. Move the balloon in your hand to various different distances, measuring the distance to the repulsion point and the repulsion force (this can be done by measuring the deflection angle of the suspended balloon and applying principles of mechanics to calculate the force).

5. Record all distances and corresponding forces.

6. Analyze the data to see if the force varies inversely with the square of the distance, as predicted by Coulomb's Law.

This experiment is a qualitative way to demonstrate Coulomb's Law, as the exact values of the charges on the balloons are not known. However, it clearly illustrates the inverse square distance relationship that is fundamental to Coulomb's Law.