Coulomb's law  (Page 23/2)

Introduction

In Grade 10, you learnt about the force between charges. In this chapter you will learn exactly how to determine this force andabout a basic law of electrostatics.

Forces between charges - coulomb's law

Like charges repel each other while opposite charges attract each other. If the charges are at rest then the force between them is known as the electrostatic force . The electrostatic force between charges increases when the magnitudeof the charges increases or the distance between the charges decreases.

The electrostatic force was first studied in detail by Charles Coulomb around 1784. Through his observations he was ableto show that the electrostatic force between two point-like charges is inversely proportional to the square of the distancebetween the objects. He also discovered that the force is proportional to the product of the charges on the two objects. That is:

where $Q_1$ is the charge on the one point-like object, $Q_2$ is the charge on the second, and $r$ is the distance between the two. The magnitude of the electrostatic force between two point-likecharges is given by Coulomb's Law .

Coulomb's Law

Coulomb's Law states that the magnitude of the electrostatic force between two point charges isdirectly proportional to the magnitudes of each charge and inversely proportional to the square of the distance between thecharges:

$$F=k\frac{Q_1{Q}_2}{r^2}$$

The proportionality constant $k$ is called the electrostatic constant and has the value:

$$k=8,99\times {10}^9\mathrm{N}·{\mathrm{m}}^2·{\mathrm{C}}^{-2}.$$

Similarity of coulomb's law to newton's universal law of gravitation.

Notice how similar Coulomb's Law is to the form of Newton's Universal Law of Gravitation between two point-likeparticles:

where $m_1$ and $m_2$ are the masses of the two particles, $r$ is the distance between them, and $G$ is the gravitational constant.

Both laws represent the force exerted by particles (masses or charges) on each other that interact by means of a field.

Next is another example that demonstrates the difference in magnitude between the gravitational force and the electrostaticforce.