Question

State Biot-Savart law.

Answer 1

Hint: It is a mathematical expression to find out the amount of magnetic field produced at a point due to the current flow in a conductor. You can define the Biot-Savart law with the following equation.

Formula used: \[dB\propto \dfrac{Idl\sin \theta }{{{r}^{2}}}\], where I is current, dl is the length of the segment of current-carrying wire, \[\theta \] is the angle that represents the orientation of the measuring point and the segment of current-carrying wire and r is the distance between the point and the segment of current-carrying wire.

Complete step-by-step answer:
Biot-Savart law is a fundamental relationship between the electric current and the produced magnetic field due to the current flow. As we know, when an electric current flows through a conductor, a magnetic field will be created. We can find out the magnetic field at a point by adding the effect of all small elements of the current-carrying conductor. Biot-Savart law can explain how the magnetic field varies with the properties of the current carrying conductor.
The magnetic field is directly proportional to the current and length of the current-carrying conductor. The magnetic field also depends upon the orientation of that point with respect to the segment of the current carrying wire. If the line from the point is perpendicular to the segment of the current-carrying wire, then the field becomes large. The field will decrease when the angle is decreased. Moreover, the distance between the point current-carrying wire is inversely proportional to the magnetic field. If the distance is twice then the magnetic field will be four times smaller.
From these pieces of information, we can develop the formula of Biot-Savart law.
\[dB\propto \dfrac{Idl\sin \theta }{{{r}^{2}}}\], where I am current, dl is the length of the segment of current-carrying wire, \[\theta \] is the angle that represents the orientation of the measuring point and the segment of current-carrying wire and r is the distance between the point and the segment of current-carrying wire.
We can use a proportionality constant, \[\dfrac{{{\mu }_{0}}}{4\pi }\], where \[{{\mu }_{0}}\] is the permeability of free space.
\[dB=\dfrac{{{\mu }_{0}}}{4\pi }\dfrac{Idl\sin \theta }{{{r}^{2}}}\]
If we are considering a current-carrying conductor in a vertical direction then we can simply define the Biot-Savart law. Then the magnetic field will be directly proportional to the current and inversely proportional to the perpendicular distance between the point and the conductor.

The diagram shows the direction of the magnetic field according to the right-hand thumb rule. The magnetic field always chooses the plane perpendicular to the line of the current segment.

Note: \[{{\mu }_{0}}\] is the permittivity of free space and it is equal to \[4\pi \times {{10}^{-7}}H{{m}^{-1}}\]. It is the resistance offered to the formation of the magnetic field in vacuum. Direction magnetic field can find out by using the right-hand thumb rule. The magnetic field always chose the plane perpendicular to the line of the current segment.