Question

State and explain the Biot-Savart law.

Answer 1

Statement and explanation of Biot-Savart law

The Biot Savart Law is used to determine the magnetic field intensity $B$ near a current-carrying conductor in terms of magnetic field intensity generated by its source current element.
Consider a wire carrying an electric current $I$ and also consider an infinitely small length of a wire $dL$ at a distance $\overrightarrow{r}$ from point $A$.Biot Savart law states that magnetic intensity $dB$ at a point $P$ due to current $dI$ flowing through a small element $dL$ is

1. Directly proportional to current$\left(I\right)$
2. Directly proportional to the length of the element $\left(dL\right)$
3. Directly proportional to $\sin \left(\theta \right)$between the direction of current and the line joining the element $dL$ from point $A$.
4. Inversely proportional to the square of the distance$\left(r\right)$ of point A from the element $dL$.
   $$\begin{gathered} dB\propto \frac{IdL\sin \left(\theta \right)}{r^2} \\ dB=k\frac{IdL\sin \left(\theta \right)}{r^2} \end{gathered}$$

where, $k=\frac{{\mu }_0{\mu }_r}{4\pi }$
${\mu }_0=$ Absolute permittivity of air in a vacuum
${\mu }_r=$ relative permittivity.