Electric Charge and Coulomb’s Law: Definition, Properties, Formula, and Examples

An atom of an element is electrically neutral, with a proton & neutron placed in the nucleus of the atom and electrons moving around the nucleus in orbit. So total positive charge on an atom is equal to the negative charge of an atom therefore atom is electrically neutral.

Electric charge and Coulomb’s law are the foundation of electrostatics. They explain how charges interact and form the basis of many concepts in electrical engineering, physics, and competitive exams like SSC JE, RRB JE, and GATE.

What is Electric Charge?

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric or magnetic field. It is measured in Coulombs (C). Subatomic particles like protons and electrons carry charge:

Proton → Positive charge (+e)
Electron → Negative charge (−e)
Neutron → No charge

The unit charge is 1.6 × 10⁻¹⁹ C.

Properties of Charge

Additivity of Charge: The total charge on a system is the algebraic sum of all charges present in it.
Example: If a body has charges +3 C, −2 C, and +1 C, then the net charge will be:
Q = (+3) + (−2) + (+1) = +2 C.

Quantization of Charge: Electric charge is always an integral multiple of the fundamental charge e (where e = 1.6 × 10⁻¹⁹ C).
q = n·e, where n = 1, 2, 3, … (integer).
Example: A body having 10 electrons will carry charge: q = 10 × (−1.6 × 10⁻¹⁹) = −1.6 × 10⁻¹⁸ C.

Conservation of Charge: Charge can neither be created nor destroyed in an isolated system; it can only be transferred from one body to another.
Example: When a glass rod is rubbed with silk, the glass rod loses electrons (becomes positively charged) while the silk gains the same number of electrons (becomes negatively charged). The total charge remains conserved.

Attractive/Repulsive Force: Like charges repel each other, whereas unlike charges attract each other. This is explained by Coulomb’s law.
Example: Two positive charges (+q, +q) placed close will push each other away, while a positive charge (+q) and a negative charge (−q) will pull each other closer.

Types of Charge

Positive Charge (+q): Carried by protons or deficiency of electrons.
Negative Charge (−q): Carried by electrons or excess of electrons.

Law of Conservation of Charge

The total electric charge in an isolated system always remains constant. If two bodies interact, the total charge before and after interaction remains the same.

Example: If a glass rod is rubbed with silk, electrons transfer from glass to silk, but the total charge remains conserved.

What is Coulomb’s Law?

Coulomb's law state that the force of attraction or repulsion between the two-point charge is directly proportional to the product of the magnitude of the two-point charge and inversely proportional to the square of the distance.
It was first observed by the Greek philosopher Thales of Miletus and then in 1785, Charles Augustin de Coulomb derived the actual mathematical relationship between the two points of charge.

Coulomb’s law states that the electrostatic force between two point charges is:

Directly proportional to the product of the magnitudes of the charges.
Inversely proportional to the square of the distance between them.
Acts along the line joining the charges.

Formula of Coulomb’s Law

The mathematical expression is:

F = k (q₁q₂) / r²

Where:

F = Force between charges (Newton)
q₁, q₂ = Magnitudes of charges (Coulombs)
r = Distance between charges (meters)
k = Coulomb’s constant = 9 × 10⁹ N·m²/C²

Case Scenarios and Examples

1. Four Charges at Square Vertices

Suppose charges of +q are placed at the four corners of a square of side a. The net force on one charge can be found by vector addition of forces due to other three charges. The diagonal forces add at 45° while side forces act along x and y axis.

2. Three Charges at Vertices of Equilateral Triangle

If charges +q are placed at each vertex of an equilateral triangle of side a, the force on one charge due to other two can be calculated. By symmetry, the resultant force bisects the angle, and magnitude is:

F = √3 * (kq² / a²)

3. Two Opposite Charges

If +q and −q are placed at distance r, the attractive force is:

F = kq² / r²

Frequently Asked Questions (FAQs)

Q1. What is the unit of electric charge?

Answer: The SI unit of charge is the Coulomb (C).

Q2. Who discovered Coulomb’s law?

Answer: Charles Augustin de Coulomb discovered it in 1785.

Q3. Is charge conserved in nuclear reactions?

Answer: Yes, even in nuclear and chemical reactions, the total charge remains conserved.

Q4. Can charge exist without mass?

Answer: No, charge is a property of matter, so it cannot exist independently without mass.

Q5. What is the difference between electric force and gravitational force?

Answer: Electric force can be attractive or repulsive, whereas gravitational force is always attractive.