Figure 29-23 shows three circuits, each consisting of two

Step 1 of 3

The Biot-Savart’s law states that the differential magnetic field intensity dH produced at a point P by the differential current element IdL is proportional to the product of IdL and the sine of the angle q between the element and the line joining the P to the element and is inversely proportional to the square of the distance R between P and the element.

\(\begin{aligned}
d H & \propto \frac{I d L \sin \alpha}{R^{2}} A / m \\
& =\frac{I d L \times a,}{4 \pi r^{2}} \\
& =\frac{I d L \times R}{4 \pi R^{3}}
\end{aligned}\)

After the integration above expression can be written as

\(H=\oint \frac{I d L \times a}{4 \pi R^{2}} A / m\)

Where \(a_{r}=\) unit vector pointing from the different elements of current to the point of interest.