Learn about Ampere’s circuital law in electromagnetism, its applications, and its extension by Maxwell. Understand the relationship between magnetic fields and electric currents.

# Ampere’s Circuital Law in Electromagnetism

Electromagnetism is the study of electromagnetic fields and their interactions with charged particles. It is a branch of physics that plays a vital role in our daily lives, from the generation of electricity to the functioning of electronic devices. One of the fundamental laws of electromagnetism is Ampere’s circuital law, which describes the relationship between the magnetic field and the electric current.

## What is Ampere’s Circuital Law?

Ampere’s circuital law, also known as Ampere’s law, states that the magnetic field created by an electric current is proportional to the electric current itself and the distance from the current. The law was first proposed by André-Marie Ampère in the 19th century and is a cornerstone of classical electromagnetism. It is expressed mathematically as:

B = μ

_{0}* I_{enc}/ 2πr

Where B is the magnetic field, μ_{0} is the permeability of free space (a constant value), I_{enc} is the electric current enclosed by the loop, and r is the radius of the loop. This equation is known as the integral form of Ampere’s law and is used to calculate the magnetic field around a closed loop.

## Applications of Ampere’s Circuital Law

Ampere’s circuital law has many practical applications, from the design of electric motors to the study of the Earth’s magnetic field. Here are some examples:

### Electric Motors

Electric motors are devices that convert electrical energy into mechanical energy. They work based on the interaction between a magnetic field and an electric current. The magnetic field is produced by a set of coils around the motor’s rotor, and the electric current is supplied through a set of brushes and a commutator. The application of Ampere’s law allows engineers to design

## Maxwell’s Extension of Ampere’s Law

In the late 19th century, James Clerk Maxwell extended Ampere’s law to include the effects of changing electric fields. He proposed that the magnetic field is not only produced by electric currents but also by changing electric fields. This led to the addition of a new term to Ampere’s law, known as the displacement current. The modified equation, known as Maxwell’s law, is given as:

∇×B = μ

_{0}* J + ε_{0}* ∂E/∂t

Where J is the current density and ε_{0} is the permittivity of free space. This extension of Ampere’s law was an essential step towards the unification of electromagnetism, as it brought together the concepts of electric and magnetic fields into a single framework.

## Conclusion

Ampere’s circuital law is a fundamental concept in electromagnetism that describes the relationship between the magnetic field and the electric current. It has many practical applications in various fields, such as electric motors and the study of the Earth’s magnetic field. The extension of Ampere’s law by Maxwell led to the unification of electric and magnetic fields and played a crucial role in the development of modern physics. Understanding the principles of Ampere’s law is essential for anyone interested in the study of electromagnetism and its applications.