Electrostatics and Coulomb’s Law Explained: Formula, Applications, and Examples

 

Introduction to Electrostatics

Electrostatics is the branch of physics that deals with electric charges at rest. It explains how charged particles interact with each other through electric forces. The study of electrostatics is one of the foundations of modern physics, electronics, electrical engineering, and material science

Everyday phenomena such as:

• Attraction of paper bits by a comb
• Lightning during thunderstorms
•  Static cling in clothes
• Dust attraction on screens

are all examples of electrostatic effects.

Electrostatics mainly focuses on:

• Electric charge
•  Electric force
•  Electric field
•  Electric potential
•  Coulomb’s law

The most important law in electrostatics is Coulomb’s law, which describes the force between two electric charges.

Historical Background

The study of electricity began in ancient Greece when people observed that rubbing amber with fur attracted small objects.

The word electricity comes from the Greek word:

 Elektron meaning amber.

Major contributors include:

•  Charles-Augustin de Coulomb
• Benjamin Franklin
• Michael Faraday
•  James Clerk Maxwell

In 1785, Coulomb experimentally established the law governing electric forces using a torsion balance experiment.

 Electric Charge

 Definition

Electric charge is the fundamental property of matter responsible for electric interactions.

Charges are of two types:

1. Positive charge

2. Negative charge

Examples:

Proton → positive

 Electron → negative

 Properties of Electric Charge

 1. Like Charges Repel

Two positive charges repel each other.

Two negative charges also repel each other.

2. Unlike Charges Attract

A positive and negative charge attract each other.

 3. Quantization of Charge

Charge exists in discrete amounts.

q = ne

Where:

• q = total charge
• n = integer
• e = electronic charge

Value of electronic charge:

e = 1.6 ×10^-19 C

 4. Conservation of Charge

Charge can neither be created nor destroyed.

It can only be transferred from one body to another.

 Methods of Charging

A body can be charged in three ways:

 1. Charging by Friction

When two objects are rubbed together, electrons transfer from one body to another.

Example:

•  Glass rubbed with silk
•  Ebonite rubbed with fur

2. Charging by Conduction

A charged object touches another object and transfers charge.

 3. Charging by Induction

A body becomes charged without direct contact.

Induction is widely used in:

• Electrostatic generators
• Capacitors
•  Electronic devices

 Conductors and Insulators

 Conductors

Materials that allow free movement of electrons.

Examples:

•  Copper
•  Silver
•  Aluminium

 Insulators

Materials that do not allow free electron movement.

Examples:

•  Rubber
•  Plastic
•  Glass

 Electrostatic Force

Electrostatic force is the force between stationary electric charges.

Characteristics:

•  Acts along the line joining charges
•  Can be attractive or repulsive
•  Depends on charge magnitude
•  Depends on distance

This force is described by Coulomb’s law.

 Coulomb’s Law

Coulomb’s law states that:

“The electrostatic 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.”

 Mathematical Expression of Coulomb’s Law

F = kq₁ q₂/r²

Where:

• F = electrostatic force
• q₁, q₂ = charges
• r = distance between charges
• k = electrostatic constant

Value of (k):

k = 9 × 10⁹ Nm^2/C²

SI Unit of Charge

The SI unit of electric charge is: Coulomb (C)

One coulomb is the amount of charge transported by a current of one ampere in one second.

Nature of Coulomb Force

 Attractive Force

When charges are unlike:

q₁ q₂ < 0       Force is attractive.

 Repulsive Force

When charges are similar:

q₁ q₂ > 0        Force is repulsive.

Vector Form of Coulomb’s Law

The force acts along the line joining the charges.

F⃗₁₂= k q₁ q₂/r²r̂

Where:

 r̂ is unit vector

 Coulomb’s Constant

The constant (k) depends on the medium.

In vacuum:

k = ¼ π ε₀

Where:

• ε₀= permittivity of free space

Value:

ε₀= 8.854 ×10^-12 C²/Nm²

 Force in a Medium

If charges are placed in a medium:

F=¼ π ε₀q₁ q₂/r²

 

Where:

• ε= permittivity of medium

Electrostatic force decreases in materials with higher permittivity.

Comparison Between Gravitational Force and Electrostatic Force

Electrostatic Force	Gravitational Force
Can attract or repel	Only attractive
Depends on charge	Depends on mass
Much stronger	Comparatively weak
Governed by Coulomb’s law	Governed by Newton’s law

 

Principle of Superposition

If several charges act on one charge, the total force equals the vector sum of individual forces.

                                                                

 F ⃗ = F ⃗ ₁+ F ⃗ ₂ + F ⃗ ₃

This principle is important in:

• Electric field calculations
•  Charge distributions
• Electrostatic systems

 Electric Field

 Definition

Electric field is the region around a charged body where another charge experiences force.

Electric field intensity:

E = F/q

Where:

• E = electric field
• F = force
• q = test charge

Unit: N/C

 Electric Field Due to a Point Charge

E = k Q/r²

Where:

• Q = source charge
• r= distance

 Electric Field Lines

Properties:

•  Originate from positive charges
•  Terminate on negative charges
•  Never intersect
•  Density represents field strength

Electric Potential

 Definition

Electric potential is the work done in bringing a unit positive charge from infinity to a point.

V = W/q

Unit: Volt (V)

Potential Due to a Point Charge

V = k Q/r

 Equipotential Surface

An equipotential surface has the same potential at every point.

Properties:

•  No work is done moving charge along it
• Electric field is perpendicular to the surface

Electric Dipole

 Definition

Two equal and opposite charges separated by small distance form an electric dipole.

Dipole moment:

p = qd

Where:

• p = dipole moment
• q = charge
• d = separation

 Electrostatic Potential Energy

Potential energy between two charges:

U = k q₁ q₂/r

Positive energy:

•  Repulsive system

Negative energy:

• Attractive system

 Capacitance

 Definition

Capacitance is the ability to store electric charge.

C = Q/V

Unit: Farad (F)

 Parallel Plate Capacitor

Capacitance:

C = ε A/d

Where:

• A = plate area
• d = separation

Applications:

• Energy storage
•  Filters
•  Electronic circuits

Applications of Electrostatics

Electrostatics has numerous practical applications.

 1. Electrostatic Precipitator

Used in industries to remove smoke and dust particles.

 2. Photocopiers

Based on electrostatic attraction.

 3. Inkjet Printing

Charged ink droplets are controlled electrically.

 4. Electrostatic Painting

Provides uniform paint coating.

5. Capacitors

Used in:

• Computers
• Radios
•  Power supplies

 6. Lightning Protection

Lightning rods protect buildings from electrical discharge.

 Coulomb’s Law Experiment

Coulomb’s Torsion Balance

Coulomb used:

• Charged spheres
• Torsion wire
• Rotational balance

Observations:

•  Force increased with charge
•  Force decreased with square of distance

The experiment confirmed inverse square law.

 Limitations of Coulomb’s Law

Coulomb’s law is valid only when:

• Charges are point charges
•  Charges remain stationary
• Distance is large compared to charge size
• Medium is uniform

It is not accurate for:

•  Moving charges
•  Quantum-scale effects

 Importance of Coulomb’s Law

Coulomb’s law forms the basis of:

•  Electrostatics
•  Electromagnetic theory
• Atomic physics
•  Electronics
•  Semiconductor devices

It also helped in the development of:

• Maxwell’s equations
•  Modern communication systems
•  Electronic engineering

Numerical Example

 Problem

Two charges: q₁ = 2 × 10^-6 C,q₂ = 3× 10^-6 C, Distance: r = 0.5 m Find electrostatic force.

Solution

Using Coulomb’s law: F = kq₁ q₂/r²

Substitute values:

F = 9 × 10⁹ × (2 × 10^-6) (3 ×10^-6)/(0.5)²

F = 9 × 10⁹ × (6 × 10^-12)/ (0.25)

F = 9 × 10⁹ × (6 × 10^-12)/ (0.25)=

F = 9 × 10⁹ ×24 × 10^-12

F = 9 × 10⁹ ×24 × 10^-12

F = 9 × 10^-3 ×24

F = 216× 10^-3

F = 0.216 N

Thus the electrostatic force is: 0.216 N

 Difference Between Electrostatics and Current Electricity

Electrostatics	Current Electricity
Charges at rest	Charges in motion
No current flow	Current flows
Static field	Dynamic field
Coulomb’s law important	Ohm’s law important

 

 Modern Applications of Electrostatics

Electrostatic principles are used in:

•  Semiconductor fabrication
•  Medical instruments
•  Touch screens
•  Laser printers
•  Particle accelerators
•  Electrostatic sensors

Nanotechnology and MEMS devices also depend heavily on electrostatic interactions.

 Conclusion

Electrostatics is one of the most fundamental branches of physics. It explains the behavior of stationary electric charges and the forces acting between them.

Coulomb’s law quantitatively describes electrostatic force and forms the basis for understanding electric fields, potential, capacitors, and many electronic systems.

From simple classroom demonstrations to advanced semiconductor technology, electrostatics plays a major role in science and engineering. The concepts developed from Coulomb’s work continue to influence modern physics, electronics, telecommunications, and industrial applications.