Charles Augustin Coulomb

Start

Charles Augustin Coulomb

A plunge into the world of attractive and repulsive forces between charged objects

In 1785 Charles-Augustin de Coulomb investigated the attractive and repulsive forces between charged objects, experimentally formulating what is now referred to as Coulomb's Law:"The magnitude of the electric force that a particle exerts on another is directly proportional to the product of their charges and inversely proportional to the square of the distance between them."In his first two articles on electricity and magnetism, Coulomb described two experiments by which he demonstrated the relation between force and distance for electrostatic charges. This relation forms an integral part of the fundamental law that today bears Coulomb’s name.In the first memoir, he described the torsion balance and his experiments to demonstrate his law for the case of electrostatic repulsion.

Introduction

TABLE OF CONTENTS

Other experiments

Coulomb's law

Results

Difficult version

Easy version

Coulomb’s Torsion balance

Coulomb’s torsion balance is an instrument designed to measure electric forces. It consists of a delicate setup within a glass case to protect it from external disturbances. Inside, a needle is suspended by a silk thread, allowing it to swing freely. At one end of the needle is a small metal sphere. A narrow glass tube extends through the case’s top, with a metal sphere positioned on its top from which the needle is suspended. Additionally, a metal rod with metal spheres at both ends passes through the top of the glass case, allowing for controlled interactions with the suspended needle.

EASY VERSION

Coulomb's Torsion Balance is a precision apparatus made up of two glass cylinders. The main cylinder is 65 cm long and includes a torsion micrometer, which sits on a larger 32 cm diameter glass cylinder with a height of 32 cm. Around the larger cylinder, an angular scale allows for precise measurements.A thin, 76 cm long metallic wire, 0.04 mm in diameter, is attached to the micrometer. This wire supports a 0.2 cm diameter copper or iron rod, which has enough weight to keep the wire taut. Attached to this rod is a sealing-wax-coated silk filament that suspends a paper disc on one end and a lightweight elder pith ball on the other.A second rod with a pith ball at its end can be inserted into the chamber through a hole near the rim of the glass plate. This setup positions the second pith ball close to the first, enabling measurement of the electrostatic forces between them.

DIFFICULT VERSION

To use Coulomb's Torsion Balance, an object with an electric charge is placed near the metal sphere at the top of a rod. The charge transfers down the rod to a sphere at the bottom, where it interacts with the needle’s sphere inside the glass case. When the rod's and needle's spheres have the same charge, they repel each other, causing the needle to move and the thread to twist. This twisting, called torsion, can be measured on a degree scale near the glass tube and the glass case’s scale, showing the needle’s movement. The amount of torsion and needle displacement increase with the charge, allowing Coulomb to quantify the electric force.Coulomb also measured repulsive forces between two similarly charged pith balls and found that these forces are inversely proportional to the square of the distance between them. He observed that if the balls had opposite charges, they would attract and stick together, making further measurement impossible. This work laid the foundation for the quantitative study of electric forces.

RESULTS

These experiments let to Coulomb's Law. It describes the electrostatic force between two charged objects. It is expressed as:​where: F is the electrostatic force, q1​ and q2​ are the charges, r is the distance between the centers of the charges, k is Coulomb’s constant, approximately 8.99×109 N⋅m2/C28.99×109N⋅m2/C2.

COUlomb's Law

To confirm the relationship between electric force and distance, Coulomb used an independent method. He suspended a charged needle with a small plate at one end and positioned it near a large hollow sphere, charged with the opposite sign. Assuming the large sphere’s charge acted as if concentrated at its center, Coulomb measured the needle’s oscillation period in response to the force between the two charges. By varying the distance and comparing it to a pendulum's motion under gravity, he related the period to the electric force, establishing that the force follows an inverse-square law with distance (Coulomb’s Law). He also showed that in conductors, all charge resides on the surface, regardless of the object's shape.

Other Experiment