Biot–Savart Law
A current element flowing up will create a B–field circulating out of the screen on the wire's
left, (represented by a circulated dot) and into the screen on the right's right, ( represented by a circulated cross).
Biot–Savart's law helps in the study of Magneto statics. This law states that the magnetic field decreases with the square of the distance from a “point of current” or current segment.
We know that electric current or moving charges are source of magnetic field. A small current carrying conductor of length dl (length element) carrying current I is a elementary source of magnetic field.
The force on another similar conductor can be expressed conveniently in terms of magnetic field dB due to the first. The dependence of magnetic field dB on current I, on size and orientation of the length element dl and on distance r was first guessed by Biot and Savart.
The magnitude of the magnetic field dB at a distance r from a current element dl carrying current I is found to be proportional to I, to the length dl and inversely proportional to the square of the distance |r|. The direction of the magnetic Field is perpendicular to the line element dl as well as radius r.
Note that both Coulomb's law and the Biot–Savart law are gauge independent : i.e., they do not depend on the particular choice of gauge. Just like Coulomb's law, the Biot–Savart law states that the field created by a bit of current is directly proportional to the amount of current, and inverse square in the distance from the current.