Biot–Savart Law

Introduction

The Biot–Savart Law is a fundamental principle in electromagnetism that describes the magnetic field generated by an electric current. Named after physicists Jean-Baptiste Biot and Félix Savart, the law provides a mathematical description of the magnetic field in terms of the current source that produces it.

Statement of the Biot–Savart Law

The Biot–Savart Law is typically formulated for a small current element, which describes an infinitesimal segment of wire carrying an electric current.

In mathematical form, the law is written as:

where:

• is the differential magnetic field at the observation location,
• is the current passing through the current element,
• is the differential length vector in the direction of the current,
• is the permeability of free space,
• is the distance from the current element to the observation location, and
• is the unit vector in the direction from the current element to the observation location.

Applications of the Biot–Savart Law

The Biot–Savart Law is essential in electromagnetism and has wide applications in physics and engineering. It is used to compute the magnetic field generated by steady currents, which are currents that do not change with time. Examples of its use include calculating the magnetic field of a circular current loop, a straight wire, and a solenoid.

Conclusion

The Biot–Savart Law is an important part of the mathematical framework of classical electromagnetism. Understanding this law is key to understanding how electric currents generate magnetic fields, and it forms the basis for many calculations in physics and engineering that involve magnetic fields.

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