A simple example of the Biot-Savart law is given with a current carrying loop for a quater of a
circle as shown in Figure 1.
Figure 1. Quarter Current Loop
The differential line element dl is perpendicular to r, so the Biot-Savart law simplifies from the
definition of the cross product
Note that the direction is into the web browser, so we have a −k. For the differential dl of a
circular arc
plugging this in and setting up the integral gives
which simply yields
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