The Biot-Savart Law finds small contributions of The Magnetic Field from small contributions of length from non-linear Current carrying wires.
After you have all the small contributions, you integrate both sides to find the total magnetic field.
Note
is a Unit Vector that gives the direction of .
For example, for a current carrying coil:
In this case
Lets plug in terms:
We can also use this to find the Magnetic Field on a long, straight, current-carrying wire, and see if it is the same as when we use Ampere’s Law.
We establish a point