Ampère's Law is a fundamental concept in electromagnetism, describing the magnetic field created by an electric current. This law relates the magnetic field an electric current creates to the current itself. Ampère’s Law, also known as Ampère’s Circuital Law, states that the total magnetic field along a closed loop is proportional to the total electric current passing through the loop. In this article, we will explore Ampère’s Law in detail, from its basic principles to its mathematical expression, and provide examples of how the law is applied in everyday life and engineering.

André-Marie Ampère

André-Marie Ampère (1775–1836) was a French physicist and mathematician who discovered the relationship between electricity and magnetism. He showed that electric currents create magnetic fields, earning him the title of "the father of electrodynamics." Ampère's observations regarding the creation of magnetic fields by electric currents preceded Faraday's work on magnetic fields, and the research of these scientists, along with Maxwell's unification of their findings, laid the foundation for modern electromagnetic theory.

^{André-Marie Ampère}

Ampère's Law states that an electric current generates a magnetic field. The law expresses that the magnetic field is proportional to the magnitude of the current, with a constant factor being the permeability of free space (μ₀). The mathematical expression of Ampère’s Law is written as:

In this equation:

• represents the line integral of the magnetic field around a closed loop.
• μ₀=4π×10⁻⁷ [H/m] is the permeability of free space, a constant.
• I_enc represents the total electric current passing through the closed loop.

This law helps us understand how magnetic fields are related to electric currents and is an important tool for calculating magnetic fields in various situations.

Determining the Magnetic Field Around a Circular Conductor

Ampère’s Law is commonly used to calculate the magnetic field around a long conductor. Let’s assume there is a long wire carrying a constant current. To determine the magnetic field around this wire, we draw an imaginary path around the wire. This path forms a circle, and we integrate the magnetic field along this path.

Since the magnetic field is the same at every point along the path due to symmetry, and the length of this path is equal to the circumference of the circle, Ampère’s Law can be used to calculate the magnetic field. The result is:

In this equation, r represents the distance from the wire, B is the magnetic field strength, and I is the current passing through the wire. Solving this equation gives us the magnitude of the magnetic field around the wire. According to this equation, the magnetic field is directly proportional to the current and decreases with distance from the wire.

Applications of Ampère’s Law

Ampère’s Law is used in various electromagnetic calculations. It has practical applications in many fields, from electrical engineering to physical research. Some important application areas of this law include:

1. Magnetic Field Around Long Current-Carrying Wires: Ampère’s Law calculates the magnetic field around long wires carrying constant currents. This is a fundamental tool for understanding the operating principles of electric motors and generators.
2. Magnetic Field Inside a Toroid: A toroid is a coil-shaped like a ring that generates a magnetic field when electric current flows through it. Ampère’s Law is commonly used to calculate the magnetic field inside toroids.
3. Magnetic Field of Conductors Carrying High Currents: Ampère’s Law is applied to calculate the magnetic fields of conductors carrying large currents. These calculations are essential for power transmission lines.
4. Magnetic Field Inside a Conductor: The magnetic field inside a conductor can be calculated using Ampère's Law. This is necessary for various applications where controlling magnetic fields is crucial.
5. Force Between Two Parallel Currents: Ampère’s Law is also used to calculate the magnetic force between two parallel conductors. The currents in the wires exert a magnetic force on each other, which is the basis for the functioning of electric motors.

Ampère’s Law is critical for understanding how electric currents create magnetic fields. It is a foundational principle in electromagnetism, one of the cornerstones of electromagnetic theory, and has wide applications in modern electrical engineering and physics. Ampère’s discoveries, along with the work of other scientists such as Faraday and Maxwell, have shaped the foundation of electromagnetic field theory. Therefore, Ampère’s Law is not only a theoretical concept but also an essential tool used frequently in modern technology.