Module 3 : MAGNETIC FIELD
Lecture 15 : Biot- Savarts' Law
Biot- Savarts' Law
Biot-Savarts' law provides an expression for the magnetic field due to a current segment. The field $\vec{dB}$at a position $\vec r$due to a current segment $I\vec{dl}$is experimentally found to be perpendicular to $\vec{dl}$and $\vec r$. The magnitude of the field is
proportional to the length $\mid dl\mid$and to the current $I$and to the sine of the angle between $\vec r$and $\vec{dl}$.
inversely proportional to the square of the distance $r$of the point P from the current element.
  Mathematically,
 
\begin{displaymath}\vec{dB} \propto I\frac{\vec{dl}\times\hat r}{r^2}\end{displaymath}
  In SI units the constant of proportionality is $\mu_0/4\pi$, where $\mu_0$is the permeability of the free space. The value of $\mu_0$is
 
\begin{displaymath}\mu_0 = 4\pi\times 10^{-7} \ \ {\rm N/amp}^2\end{displaymath}
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