Question

The relation between magnetic field and current is given by Biot-Savart law. Illustrate Biot-Savart law with necessary figure.

Answer 1

According to Biot-Savart Law, magnetic field due to an element carrying current $I$ in the direction $\overrightarrow{dl}$ at a point $\overrightarrow{r}$ from the element is given by:

$\overrightarrow{dB}=\frac{{\mu }_{o}I}{4\pi r^3}(\overrightarrow{dl}\times \overrightarrow{r})$

Biot-Savart Law can be explained by the attached figure. Consider a wire carrying current $I$. To find the net magnetic field due to the wire at point P, a small element of length $\overrightarrow{dl}$ is chosen and its magnetic field $\overrightarrow{dB}$ is found using the Biot-savart law as mentioned above. The net magnetic field at the point $P$ can be found by integrating the magnetic field at $P$ over complete length of wire. It must be noted that direction of the magnetic field can be quickly found using the right hand thumb rule.