Mastering Coulomb's Law for JEE Physics

Welcome to this module on Coulomb's Law, a cornerstone of electrostatics and crucial for your JEE Physics preparation. This law quantifies the force between two stationary, electrically charged particles. Understanding it is key to solving a wide range of problems in electromagnetism.

The Fundamental Concept: Electric Charge

Before diving into Coulomb's Law, let's recap electric charge. Charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative. Like charges repel each other, while unlike charges attract each other. The SI unit of electric charge is the Coulomb (C).

What are the two types of electric charge, and what is the SI unit of charge?

The two types are positive and negative. The SI unit is the Coulomb (C).

Introducing Coulomb's Law

Coulomb's Law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. This force acts along the line joining the two charges.

Force between charges depends on charge magnitude and distance.

The force is stronger if the charges are larger and weaker if they are farther apart. Specifically, it decreases with the square of the distance.

Mathematically, Coulomb's Law can be expressed as: $F = k \frac{|q_1 q_2|}{r^2}$ , where $F$ is the magnitude of the electrostatic force, $q_1$ and $q_2$ are the magnitudes of the two charges, $r$ is the distance between their centers, and $k$ is Coulomb's constant. Coulomb's constant, $k$ , is approximately $8.9875 \times 10^9 N m^2/C^2$ . It can also be expressed in terms of the permittivity of free space, $\epsilon_0$ , as $k = \frac{1}{4\pi\epsilon_0}$ .

Visualizing Coulomb's Law: Imagine two point charges, $q_1$ and $q_2$ , separated by a distance $r$ . The force between them is a vector. If the charges are of the same sign (both positive or both negative), the force is repulsive, pushing them away from each other along the line connecting them. If the charges are of opposite signs (one positive, one negative), the force is attractive, pulling them towards each other along the same line. The strength of this force is governed by the formula $F = k \frac{|q_1 q_2|}{r^2}$ . This means doubling either charge doubles the force, while doubling the distance reduces the force to one-fourth.

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Key Components of Coulomb's Law

Component	Description	Impact on Force
Magnitude of Charges ( $\|q_1\|, \|q_2\|$ )	The absolute value of the electric charge on each particle.	Directly proportional: Larger charges exert stronger forces.
Distance between Charges ( $r$ )	The separation between the centers of the two point charges.	Inversely proportional to the square: Doubling the distance reduces the force by a factor of 4.
Coulomb's Constant ( $k$ )	A proportionality constant that depends on the medium. For vacuum, $k \approx 8.9875 \times 10^9 N m^2/C^2$ .	Determines the overall strength of the electrostatic force.

Vector Nature of Electrostatic Force

While the formula gives the magnitude, the electrostatic force is a vector quantity. It has both magnitude and direction. The direction is along the line joining the two charges. For multiple charges, the net force on a charge is the vector sum of the forces exerted by each individual charge (Principle of Superposition).

Remember the inverse square law! The force drops off rapidly as the distance increases.

Applications and JEE Relevance

Coulomb's Law is fundamental to understanding electric fields, electric potential, capacitance, and many other concepts in electromagnetism. JEE problems often involve calculating the net force on a charge in the presence of multiple charges, or determining the equilibrium positions of charges. Mastering the vector nature and the inverse square relationship is crucial for success.

If you triple the distance between two charges, by what factor does the electrostatic force change?

The force decreases by a factor of $3^2 = 9$ .

Practice Problems

To solidify your understanding, practice problems involving:

Calculating force between two point charges.
Finding the net force on a charge due to multiple charges (superposition).
Determining equilibrium conditions for charges.
Understanding the effect of changing distances and charge magnitudes.

Learning Resources

Coulomb's Law - Physics Classroom(documentation)

A comprehensive explanation of Coulomb's Law, including its mathematical formulation and conceptual understanding, with clear diagrams.

Coulomb's Law - Khan Academy(video)

An introductory video explaining Coulomb's Law, its formula, and how to apply it with examples.

Coulomb's Law and Electric Field - MIT OpenCourseware(paper)

Lecture notes from MIT covering Coulomb's Law and its relation to electric fields, suitable for advanced understanding.

Understanding Coulomb's Law - Brilliant.org(blog)

An interactive explanation of Coulomb's Law, focusing on conceptual clarity and problem-solving techniques.

Electric Force and Coulomb's Law - HyperPhysics(documentation)

A concise and well-organized overview of electric force and Coulomb's Law, with links to related concepts.

JEE Physics: Electrostatics - Coulomb's Law Problems(video)

A video tutorial specifically focused on solving JEE-level problems related to Coulomb's Law.

Coulomb's Law - Wikipedia(wikipedia)

A detailed article on Coulomb's Law, covering its history, mathematical formulation, and applications in physics.

Electric Charge and Coulomb's Law - Vedantu(blog)

An educational resource explaining electric charge and Coulomb's Law with examples relevant to competitive exams.

Coulomb's Law Explained - Physics LibreTexts(documentation)

A chapter from an open-source university physics textbook detailing Coulomb's Law and its applications.

Practice Problems on Coulomb's Law - Toppr(blog)

A collection of solved practice problems on Coulomb's Law, designed to help students prepare for exams.