# Biot – Savart law

Biot – Savart law and its Application to Current Carrying Circular Loop

Biot-Savart’s law is the equation used for representing the magnetic field, produced due to a segment that is carrying the current. The segment that is carrying current is taken as the vector quantity. A magnetic field is produced by the current-carrying circular conductor loop around its axis, and this phenomenon is defined as the Biot Savart’s law. Here R represents the radii of the loop, and X is used to represent the distance from the axis through the center. In the setup that is shown in the figure, three conductor loops are having the different radii and are mounted on the special loop holder which is provided for the investigation purpose. By using the axial hall probe, the magnetic radii can be measured. There is the provision of the high current power supply, for the production of the magnetic field.

## Examples of the Biot Savart’s Law

Consider the current-carrying loop, having the radius R and the current I flowing through it. The electric field at the distance I from the center of the loop due to the smaller elements’ ds can be stated according to the Biot Savart’s law as follows.

d→B = μ04π id→s ×^rr2

Let consider that the current-carrying element ids are at the M position that is coming out of the plane. Diametrically, the loop can be divided into the to the opposite pairs.

α = θ

∴ cos θ = R√R2 + l2

Thus,

dB cos θ = μ04π i dsR2 + l2 × R√R2 + l2

Then the total field values will be as followings

B = μ0 i R22(R2 + l2)32

## Applications of the Biot Savart’s Law This

This law is used for the calculation of magnetic reactions even at the atomic or molecular level. It can also be used in the aerodynamics theory, for determination of the velocity, encouraged due to the vortex lines. In the aerodynamic applications, the role of current and velocity are reversed, as compared to the magnetic application. In the paper of Maxwell, in 1861 on the physical lines of force, the magnetic field strength is directly equated with the pure spin (velocity), whereas, B is the weighted velocity that is weighted for the density of vortex sea. According to the consideration of Maxwell, the magnetic permeability is the measure of the density of vortex sea. So, it can be used to find the relationship between the magnetic induction current, and electric convention current.