Biot- Savarts' Law
2 min read
Biot- Savarts' Law: Biot-Savarts' law provides an expression for the magnetic field due to a current segment. The field at a position
due to a current segment
is experimentally found to be perpendicular to
and
. The magnitude of the field is
-
proportional to the length
and to the current
and to the sine of the angle between
and
.
-
inversely proportional to the square of the distance
of the point P from the current element.
![\begin{displaymath}\vec{dB} \propto I\frac{\vec{dl}\times\hat r}{r^2}\end{displaymath}](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image008_0008.gif)
In SI units the constant of proportionality is
, where
is the permeability of the free space. The value of
is
![$\mu_0/4\pi$](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image009_0009.gif)
![$\mu_0$](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image010_0006.gif)
![$\mu_0$](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image010_0007.gif)
![\begin{displaymath}\mu_0 = 4\pi\times 10^{-7} \ \ {\rm N/amp}^2\end{displaymath}](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image011_0004.gif)
-
The expression for field at a point P having a position vector
with respect to the current element is
![](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/Lec-15/images/15.1_3_clip_image002.gif)
![](https://raw.githubusercontent.com/xibsked/menka/master/books/physics-for-engineers-2/4e15457225ac3dc33d1a7f8228fc12b81.png)
For a conducting wire of arbitrary shape, the field is obtained by vectorially adding the contributions due to such current elements as per superposition principle,
where the integration is along the path of the current flow.
![\begin{displaymath}\vec B(P) = \frac{\mu_0}{4\pi}I\int\frac{\vec{dl}\times\hat r}{r^2}\end{displaymath}](http://www.cdeep.iitb.ac.in/nptel/Core Science/Engineering Physics 2/Slides/Module-3/main3_clip_image014_0003.gif)