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:
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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.
FAQs on Coulomb
1. What is Coulomb's Law in Physics?
Coulomb's Law is a fundamental principle in electrostatics that describes the force between two stationary point charges. It states that this force is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance separating them. The force acts along the straight line connecting the charges.
2. How is one coulomb (1 C) of charge defined?
One coulomb is the standard SI unit of electric charge. It is defined as the amount of charge that, when placed 1 metre away from an identical charge in a vacuum, results in an electrostatic force of 9 × 10⁹ Newtons. In practical terms, 1 C is equivalent to the total charge of approximately 6.242 × 10¹⁸ electrons.
3. What are the most important limitations of Coulomb's Law?
While fundamental, Coulomb's Law has specific limitations and is not universally applicable. Key limitations include:
- Applicable only to stationary charges: The law accurately describes electrostatic force but does not apply to charges that are in motion.
- Requires point charges: The formula is precise for point charges or spherically symmetric charge distributions. It becomes complex to apply directly to irregularly shaped charged bodies.
- Valid at specific distances: It holds true for atomic and macroscopic distances but breaks down at sub-nuclear distances (less than 10⁻¹⁵ m), where the strong nuclear force becomes dominant.
4. How does Coulomb's Law differ from Newton's Law of Gravitation?
Both are inverse-square laws, but they have crucial differences:
- Type of Force: Gravitational force is always attractive, whereas the electrostatic force described by Coulomb's Law can be either attractive (for unlike charges) or repulsive (for like charges).
- Strength of Force: The electrostatic force is significantly stronger than the gravitational force.
- Dependence on Medium: The electrostatic force is affected by the medium between the charges (characterised by permittivity), while the gravitational force is independent of the intervening medium.
5. Why is the vector form of Coulomb's Law important for solving Physics problems?
The vector form of Coulomb's Law is essential because force is a vector quantity. It provides not only the magnitude of the electrostatic force but also its precise direction. This is critical when calculating the net force on a charge in a system with multiple charges, as it allows us to use the Principle of Superposition to find the vector sum of all individual forces acting on the charge.
6. How does placing charges in a medium like water affect the force calculated by Coulomb's Law?
Placing charges in a dielectric medium (like water, oil, or glass) reduces the electrostatic force between them compared to the force in a vacuum. The force is reduced by a factor known as the dielectric constant (K) or relative permittivity of that medium. The new force in the medium is calculated as F_medium = F_vacuum / K. This happens because the molecules of the medium get polarised and create an opposing electric field.
7. Is 1 joule equal to 1 coulomb?
No, a joule and a coulomb are not equal; they measure different physical quantities. A coulomb (C) is the unit of electric charge. A joule (J) is the unit of energy or work done. The two are related through electric potential (voltage), where one joule is the work required to move a one-coulomb charge across a potential difference of one volt (1 J = 1 C × 1 V).
