Here we will examine two examples of the Biot-Savart law, one simple and the other more
challenging. To begin we will find the magnetic field at the center of a current carrying loop as
shown in figure 1
Figure 1:Figure 1: Current Loop
this setup is the same as the quater loop example of Biot-Savart law where we have
giving us a similar integral, except from 0 to 2 π and the lack of a minus sign since the
current is going in the opposite direction so the magnetic field will be out of the web
browser
taking the integral gives the magnetic field at the center of the loop
The second more challenging example is the magnetic field at a point z above the loop as shown in
figure 2
Figure 2:Figure 2: Current Loop
The not so obvious hint is the direction of dB. The cross product of r with dl leads to a vector
perpendicular to both of them and as you go around the loop, dB will always be off the z axis by
an angle ϕ. This makes all the horizontal components of dB cancel leaving just the vertical
so
This is version 4 of loop example of Biot-Savart law, born on 2006-01-14, modified 2011-01-18.
Object id is 105, canonical name is LoopExampleOfBiotSavartLaw.
Accessed 11557 times total.
![[parent]](https://images.physicslibrary.org/images/uparrow.png)
