Coulomb constant

Introduction

The Coulomb constant, also known as the electrostatic constant, is a fundamental constant in electrostatics. It is denoted by the symbol k or ke, and has a value of approximately 8.9875517923(14)×10^9 N(m/C)^2. This constant is a measure of the amount of force between two charges separated by a distance in a vacuum. It is named after the French physicist Charles-Augustin de Coulomb who first formulated Coulomb's Law, which describes the electrostatic interaction between electrically charged particles.

Physical Significance

The Coulomb constant is an important factor in the calculation of electrostatic forces between charged particles. According to Coulomb's Law, the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The Coulomb constant is the proportionality constant in this equation.

Mathematical Representation

In mathematical terms, the Coulomb constant is represented in Coulomb's Law as follows:

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

where:

F is the force between the charges,
q1 and q2 are the amounts of charge,
r is the distance between the charges,
k is the Coulomb constant.

Units and Dimensions

The Coulomb constant has the units of N(m/C)^2 in the SI system. This can also be expressed as kg*m^3/s^2*C^2. The dimensions of the Coulomb constant are [M L^3 T^-2 I^-2] in the dimensional notation.

Experimental Determination

The value of the Coulomb constant can be determined experimentally using a torsion balance experiment, similar to the one conducted by Henry Cavendish to measure the gravitational constant. The experiment involves measuring the tiny torsional force exerted by two small charged spheres on a horizontal bar suspended by a thin wire.

Relation to Other Physical Constants

The Coulomb constant is related to other physical constants such as the speed of light (c) and the permittivity of free space (ε0). The relation is given by the equation:

k = 1 / (4πε0)

This relation shows that the Coulomb constant is not an independent constant, but is derived from other fundamental constants.

Applications

The Coulomb constant is used in various fields of physics and engineering, including electrostatics, electrodynamics, and quantum mechanics. It is essential in calculations involving electric fields, electric forces, and potential energy of charged particles.