A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field.

The Biot–Savart law is an equation describing the magnetic field generated by an electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The law is valid in the magnetostatic approximation and is consistent with both Ampère’s circuital law and Gauss’s law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart who discovered this relationship in 1820.

 Topical Notes
Forces on moving charges in magnetic fields
Forces on current-carrying wires in magnetic fields          
Fields of long current-carrying wires
Biot-Savart law and Ampere’s law
                                                               Test your Understanding: Chapter 4 MCQ Quiz 1 Here                                                                                                     Take Chapter 4 ReQuiz MCQ Quiz 2 Here 

The Biot–Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I (for example due to a wire): a continual flow of charges which is constant in time and the charge neither accumulates nor depletes at any point. The law is a physical example of a line integral, being evaluated over the path C in which the electric currents flow.

Earth Magnetic field