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In 1820, two French scientists Jean Baptiste Biot and Felix Savart experimented with the interaction between an electric current and a magnetic field.
Every magnetic field is produced by a current and the intrinsic magnetic movements of the particles. Thus the relation between the arbitrary current and magnetic field is referred to by the Biot-Savart law.
What is the Biot-Savart law?
The interaction between a straight, current carrying magnet is given by the Biot-Savart law, which is understood by: a conductor XY carrying a current I, has a magnetic field dB is determined at a point P, which is at a distance r from it. The angle between dl and r is . This is expressed as:
From the formula of the Biot-Savart law, we know that:
The magnitude of dB is directly proportional to the current I and the element length dl .
The magnetic field dB is inversely proportional to the square of distance r. The direction is perpendicular to the plane containing dl and r.
The magnitude of dB is written as:
Hence, if the value of is 0, then the dB will also be 0.
The magnetic field B of an element dl, with a current carrying wire is given by:
Relationship between Biot-Savart law and Coulomb’s law
There are some similarities as well as differences between the Biot-Savart law for a magnetic field and Coulomb’s law for an electrostatic field.
Both the laws are of long range as both are inversely proportional to the distance from the source to the point.
The electrostatic field is produced by a scalar source called electric charge and the magnetic field is produced by a vector source called Idl.
The electrostatic field is along the displacement vector, which joins source and field point. The magnetic field is perpendicular to the plane, which contains the displacement vector and current element.
The Biot-Savart law depends on angles while the electrostatic field in Coulomb’s law is independent of angles. The magnetic field at any point in the direction of dl is zero. Hence the dB will be zero.
Also there is an relationship between 0 and 0and the speed of light c. That is shown from the following equation:
Steps to be followed while calculating problems using Biot-Savart’s law
See whether the given problem can be solved by the Biot-Savart law. But if there’s a symmetry in B and dl, then use Ampere’s law. If there’s not enough symmetry then use the Biot-Savart law.
Draw dl and r in such a manner that dl points towards the direction of current and r from the direction of the current element towards the point where the magnetic field is desired.
- Calculate the product of dlr, which gives the direction of the magnetic field according to this law.
5.Finally, the right-hand rule will be used to verify the direction of the magnetic field that is produced from the current.
Simple example to calculate magnetic field
If an element l=xi placed at origin and carries current I=10A , the magnetic field on the y – axis at distance of 0.5 m and x =10-²m is calculated as follows:
The magnetic field is calculated by using the Biot-Savart law formula
Application of Biot-Savart law
The Biot-Savart law is applied in a magnetic field on the axis of a circular loop:
The magnetic field at point P due to a circular loop is given by the formula
Where x²+ R² is the distance from the point P.
2.Magnetic field due to a finite straight wire:
The magnetic field at a point P due to a straight finite wire is given by the formula
Conclusion
This article explains Biot-Savart law. The relation or interaction between the magnetic field and current is defined through the Biot-Savart law. Every magnetic field is produced by a current and the intrinsic magnetic movements of the particles. Thus the relation between the arbitrary current and magnetic field is referred to by the Biot-Savart law.
