Ampère's Law, Formula and Example of Applications

Ampère's law is one of the fundamental laws of classical electrodynamics. This law was formulated by Andre Marie Ampère in 1826.

Ampère's law states:

• The circulation of the magnetic field of constant currents along any closed circuit is proportional to the sum of the forces of the currents that cross the surface of the circuit.

• If direct current is used, the magnetic field is continuous.

• If alternating current is used, the magnetic field is alternating.

Ampère's Law Formula

Ampère's law can be represented by the following equation:

In this formula for calculating the magnetic field, the integral represents the circulation of the field lines along a closed path, and:

• μ0 is the permeability of the vacuum

• dl is a vector tangent to the path chosen at each point

• IT is the net current intensity that passes through the surface delimited by the path, and it will be positive or negative depending on the direction in which it crosses the surface.

Example of Application of Ampère's Law: the Electromagnet

An electromagnet is a type of magnet that is activated when an electrical current flows through it. Usually, electromagnets are made up of a large number of turns of wire very close to each other.

If the ends of this wire are connected to a potential difference, electric current flows through it and a magnetic field is generated.

This magnetic field is equivalent to the sum of the magnetic fields of each loop and can be calculated by applying Ampère's law.

Attraction Force Between Conductors with Electric Current

Two conductors influence each other. Parallel and rectified electric currents attract each other, parallel and opposite currents repel.

This can be understood in terms of the Lorentz force: the current in one wire generates a magnetic field which, due to Lorentz's law, produces a force on the moving charges in the other wire and therefore both wires they feel a mutual force.

What Are Maxwell's Laws?

After the discovery of Ampère's law, Maxwell summarized the entire theory of electromagnetism in four equations: Maxwell's laws.

Ampere's law, with an extension for a time-dependent dielectric shift, is one of them. However, Maxwell's laws are often written in differential form, that is, not with integrals as before, but equations that give relationships between the derivatives of the electric and magnetic fields.

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Published: September 15, 2021
Last review: September 15, 2021