PlanetPhysics/Quarter Loop Example of Biot Savart Law
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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.
\begin{figure} \includegraphics[scale=.8]{QuarterCurrentLoop.eps} \vspace{10 pt} \caption{Figure 1: Quarter Current Loop} \end{figure}
The differential line element d{\mathbf l} is perpendicular to , 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 . For the differential dl of a circular arc
plugging this in and setting up the integral gives
which simply yields