Derivation Of Biot Savart Law: Application, Importance, FAQ

Biot-Savart Law is a fundamental principle in electromagnetism that describes the magnetic field generated by a current-carrying conductor. It states that the magnetic field at a point P due to a current-carrying segment is proportional to the product of the current, the length of the segment, and the sine of the angle between the direction of the current and the line connecting the point P to the segment.

The law is used to calculate the magnetic field generated by various configurations of current-carrying conductors, such as wires and coils.

Biot Savart Law

Biot-Savart Law is a fundamental principle in electromagnetism that describes the magnetic field generated by a current-carrying conductor.

The law is named after Jean-Baptiste Biot and Félix Savart who derived it in 1820.

The law states that the magnetic field dB at a point P due to a small element of current dl at a point Q is proportional to the product of current, the sine of the angle between the direction of current and the line joining P and Q, and the inverse of the distance between the two points cubed

dB =

where: μ₀ is the vacuum permeability (a constant), dl is the current element, r is the distance between them.

The biot-savart law forms the basis for calculating the magnetic fields generated by electrical currents in wire and coils, and also provides insight into the interaction between magnetic fields and electric currents.

Derivation of Biot Savart Law

Biot Savart law can be derived as-

By using electric fields which are generated by stationary charges we get

E = 0

E = –

Where

Φ = electric scalar potential

The expression which is obtained by electric fields that are generated by stationary charges is

E(r) = (r’)( ) d³r’

Below is the Biot-Savart law expression before putting the value of j

B(r) = ( ) d³r’

By putting the value of j (current density) where I is the vector current and dl is element length

j(r) d³r = I(r) dl

After substituting the value of j

we obtain the Biot-Savart expression

B(r) = ( ) d³r’

Application of Biot Savart Law

Biot-Savart Law has several applications in different fields of science and engineering.

Some important application of Biot Savart Law are given as-

The Biot Savart Law is used for calculating magnetic responses at the molecular levels.

This law is used in aerodynamic theory while calculating velocity generated by vortex lines.

It is used to calculate atomic and molecular magnetic responses.

Importance of Biot Savart Law

Biot-Savart Law is an important concept in physics because it provides a way to calculate the magnetic field generated by a current-carrying conductor.

This law has several important applications in various fields, including electromagnetism, electromagnetic induction, electromagnetic waves, plasma physics, astrophysics, particle accelerator design, and electromagnetic shielding.

The main importance of Biot Savart law is given as-

The Biot Savart law is applied on small conductors which carry electric current.

Biot savart law is also applied to symmetrical current distribution.

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