How to do Biot-Savart for Multiple Currents - Yikes!!

Here it is...this can be for many students, the toughest part of magnetism.  Biot-Savart (B-S) integrals for currents.  Keep in mind B-S is the general law for finding magnetic fields from moving charges, and when there is a current, i.e. many moving charges, we need to add up a bunch of small B-fields to get the total - that means an integral!

Check out this video as an example for two currents.  This means two magnetic fields, and therefore two integrals.  Replay it as necessary, try to work along with it, to get the hang of constructing the integrals needed for a specific problem.  Typically the thing that changes from problem to problem is the location of the point we are looking at, so that changes the bounds on the integrals.  But the construction is pretty much the same process every time.  FOCUS ON THE PROCESS used to construct each of the integrals, and that will help...that is the physics.  I'm not even going to show the solutions of the integrals, because that is math; learn the physics here!