This law was named after Jean-Baptiste Biot and Felix Savart in 1820. They derived the mathematical expression for the magnetic flux density.

The Biot-Savart Law is an equation that explains the magnetic field created by a current carrying wire, allowing the calculation of its strength at various points. This is because when a compass is moved near an electric wire, the compass needle tends to change the direction.

EXPLANATION

It relates the magnetic field to direction, length, magnitude and proximity of the current. The law is valid in magnetostatic approximation. This law comes in handy while calculating the magnetic field that results from an electric current distribution.

The magnetic intensity at any given point owing to a steady current in a straight and long wire is-

- Directly proportional to the current flowing
- Inversely proportional to the distance of wire from point

This law is consistent with Ampere’s circuital law and also Gauss’s law for magnetism.

EQUATIONS

- Electric currents along closed curve

Where,

B= magnetic field

R= position

I= steady current

C= path in which electric current flows

dl= vector whose magnitude is equal to the length of differential element of wire in direction of the conventional current, r’=r-l, the full displacement vector from the wire element (l) to the point where the field is being computed (r)

is a magnetic constant

- Electric currents throughout the conductor volume

When the conductor has some thickness, the equation is given as-

Where, dV is the volume element

J is the current density in that volume

- Biot Savart law for a point charge

Where, is the unit vector that points to the current position of the particle to the very point at which the field gets measured

APPLICATIONS OF BIOT SAVART LAW

- This can be used to calculate magnetic response at atomic or molecular level, provided that current density is given.
- It can also be used in aerodynamics to calculate the velocity which is induces by the vortex lines.

THE BIOT SAVART LAW, AMPERE’S CIRCUITAL LAW, GAUSS’S LAW FOR MAGNETISM

- In a magnetostatic situation-

The magnetic field B as obtained from the Biot-Savart law, manages to always obey Ampere’s law and Gauss’s law for magnetism.

- In a non-magnetostatic situation,

Even though Gauss’s law for magnetism and Maxwell-Ampere’s law holds true, the Biot-Savart law fails to be true.