# Coulomb

A French Military Engineer and Physicist named Charles-Augustin de Coulomb brought the concept of electrostatic forces (attractive and repulsive) between two charges placed inline apart with a square of the distance that lies inversely proportional to this force; however, the product of two charges always remains directly proportional to this force. This statement is called Coulomb’s law.

In International Systems or SI systems, the unit of an electric charge is Coulom. The unit was so named as an honour to Mr Coulomb in 1880 after the discovery of Coulomb’s law by him in 1785.

### Coulomb’s Law

According to Coulomb’s law, if two charges are separated by a distance ‘r’, and the charges are of opposite polarities as well. The distance between the two charges remains constant. So, when these charges apply forces on each other, they generate a force, which is the electrostatic force of attraction, as the charges are of the same magnitude but with different polarities.

If there were charges of the same magnitude, also the same polarities, then there would have an electrostatic force of repulsion between them because these charges are static and are joined together with an imaginary line.

So, in both cases, the equation remains the same for the force and that is:

F α $\frac{q1q2}{r^{2}}$

As the force remains proportional to the product of charges and the square of the distance between these, so, on removing the sign of proportionality constant, we generate the following new form of the above equation:

F = k $\frac{q1q2}{r^{2}}$

Here, k is the proportionality constant called the Columb’s law Constant, and its value is calculated in the following manner:

### Coulomb’s Law Constant Value

From the above equation, we can re-arrange to determine the value of k:

k = $\frac{1}{4 \pi \epsilon_{0}}$ ….(2)

We know that the value of the dielectric constant, or the electric permittivity at free space is 8.85 x 10⁻¹² C²/Nm². Now, putting this value in equation (2), we get:

k = $\frac{1}{4 \times 3.14 \times 8.85 \times 10^{-12} (C^{2} /Nm^{2})}$

On solving, we get the value of k = 8.99 x 10⁹Nm²C⁻²

### 1 Coulomb

In an International Systems, the unit of electric charge is the meter-kilogram-second-ampere, which is the basis of the SI system of physical units. Coulomb is abbreviated as C. Coulomb unit is of the electric charge.

We define Coulomb as the quantity of electricity transported in one second by a current of one ampere. This quantity was named Coulomb in the 18th–19th-century after a French physicist named Charles-Augustin de Coulomb, one Coulomb is approximately equal to 6.25 × 1018 electrons.

### 1 Coulomb Charge

So, from the above statement of 1 Coulomb, we understood that the value of 1 Coulomb charge is equal to 6.25 x 10¹⁸ or 6.24 quintillion electrons.

Let’s understand the Coulomb SI unit in detail:

Let’s suppose that there are millions of charges flowing through a copper wire in the following manner:

Now, why do Physicist use such a big unit for a charge? Well! Its understanding is easy by going more in mathematics beyond it.

When the current of 1 ampere flows through this wire, 1 Coulomb of electrons, i.e.,  6.25 x 10¹⁸ electrons pass through it every second, i.e., given by:

1C/1 sec = 1 Amp

So, we could clearly define one Coulomb from the above statement.

### One Coulomb Charge Formula

According to the law of conservation of charges, whatever electrons flow through the wire, are quantized and also they remain conserved. So, if there are ‘n’ number of electrons flowing through a wire where ‘e’ is an elementary charge of the magnitude, i.e., 1.6 x 10⁻¹⁹ C. The ‘q’ is a charge of 1 C, the formula is:

q = ne

For the number of electrons, we re-write the equation in the following way:

n = q/e

### Derive One Coulomb Charge Value

Let’s say an electrical circuit carries a charge of the magnitude 1.6 x 10⁻¹⁹ C.

When the charge is 1.6 x 10⁻¹⁹ C , the number of electrons = 1

Now, if the charge is 1 C, then the number of electrons will be  = 1/1.6 x 10⁻¹⁹ C

On Solving, we get the value of 1 Coulomb charge as 6.25 x 10¹⁸.

So, in 1 C, the number of electrons flowing through the above copper wire is 6.25 x 10¹⁸. This is the sole reason why Physicists use a huge unit like Columb for lump sump of electrons flowing through a wire.

Fun Fact

In a house, ordinarily, we use a 100-watt power lightbulb that draws out 1 ampere of current. Here, Coulombs come in handy for measuring the charges held by household electrical circuits.

Q1: What is Coulomb’s Law in a Vector Form? Is Coulomb’s Law Experimental in Nature?

Ans: The vector form of Coulomb’s law has great importance when there is an arrangement of point charges separated by a distance.

In this case, the resultant force on any one of the charges is the vector sum of the forces because of each of these other forces; the science beyond this phenomenon is called the principle of superposition.

Yes, Coulomb’s law is experimental in nature. It is because this law quantifies the amount of force that exists between two stationary or static electrically charged particles. Furthermore, electrostatic force or Coulomb force refers to the electric force which exists between point charges that are at rest position.

Q2: What Does Coulomb’s Law Describe?

Answer: Coulomb’s Law gives us an idea about the force between the two-point charges that are inline with each other separated by some distance. By the word point charge, we mean that the size of linear charged bodies is very small or you can say negligible as compared to the distance between them. That’s why we consider these charges as points, as it becomes easy for us to calculate the force of attraction or repulsion between them.

From this theory, we infer that like charges repel each other and unlike charges attract each other. This means charges of the same sign/polarity pushes each other with repulsive forces while charges with opposite signs pull each other with attractive force.