Biot-Savart Law

Summary:

The Biot-Savart Law is a fundamental principle that describes the magnetic field produced by a steady electric current. It establishes a relationship between the magnetic field and various parameters such as the magnitude, direction, length, and proximity of the electric current. The Biot-Savart Law is consistent with Ampere’s circuital law and Gauss’ theorem and plays a significant role in magnetostatics, similar to Coulomb’s law in electrostatics.

The Biot-Savart Law was formulated by Jean Baptiste Biot and Felix Savart in 1820. Through observations and calculations, they derived a mathematical expression that relates the magnetic field intensity (dB) at a point to the length of the current-carrying element (dl), the current (I), the sine of the angle (θ) between the current and the vector joining the point to the element, and the inverse square of the distance (r) from the point to the element.

The Biot-Savart Law can be expressed as dB = (μ0/4π) × (I dl × sinθ)/r^2, where μ0 is the permeability of free space.

Considering a long wire carrying current I and a point P in space, the magnetic field at point P due to a small length dl of the wire is directly proportional to the current and inversely proportional to the square of the distance. The angle θ between the distance vector r and the current contributes to the magnetic field as well.

By integrating the contributions from all the small elements of the wire, the expression for the magnetic field at point P due to the entire length of the wire can be obtained.

Excerpt:

Biot-Savart Law

The Biot Savart Law is a condition portraying the attractive field created by a consistent electric flow. It relates the attractive field to the extent, bearing, length, and nearness of the electric flow. Biot-Savart regulation is steady with both Ampere’s circuital regulation and Gauss’ hypothesis. The Biot Savart regulation is key to magnetostatics, assuming a part like that of Coulomb’s regulation in electrostatics.