Magnetics
12.0 Biot Savart Law
12.0 Biot Savart Law
The Biot Savart Law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. Biot–Savart law is consistent with both Ampere’s circuital law and Gauss’s theorem. The Biot Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb’s law in electrostatics.
Biot Savart Law states that
The magnetic intensity $dH$ at a point $A$ due to current $I$ flowing through a small element $dl$ is
1. Directly proportional to current $(I)$
2. Directly proportional to the length of the element $(dl)$
3. Directly proportional to the sine of angle $θ$ between the direction of current and the line joining the element $dl$ from point $A.$
4. Inversely proportional to the square of the distance $(x)$ of point $A$ from the element $dl.$$$dH = \frac{{{\mu _0}{\mu _r}}}{{4\pi }} \times \frac{{I\;dl\sin \theta }}{{{x^2}}}$$$$dH = K \times \frac{{I\;dl\sin \theta }}{{{x^2}}}$$$$dH \propto \frac{{I\;dl\sin \theta }}{{{x^2}}}$$where $k$ is constant and depends on the magnetic properties of the medium.$$K = \frac{{{\mu _0}{\mu _r}}}{{4\pi }}$$$\mu_0 =$ absolute permeability of air or vacuum and its value is $$\frac{{4 \times {{10}^{ - 7}}Wb}}{{A - m}}$$$\mu_r =$ relative permeability of the medium.
Importance of Biot-Savart Law
Following are the importance of Biot-Savart law:
$ \bullet $ Biot-Savart law is similar to the Coulomb’s law in electrostatics.
$ \bullet $ The law is applicable for very small conductors too which carry current.
$ \bullet $ The law is applicable for symmetrical current distribution.
Applications of Biot-Savart’s Law
Some of Biot-Savart’s Law applications are given below.
$ \bullet $ We can use Biot–Savart law to calculate magnetic responses even at the atomic or molecular level.
$ \bullet $ It is also used in aerodynamic theory to calculate the velocity induced by vortex lines.
