# Biot-Savart Law | Statement, Derivation, Use and Example

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## Biot-Savart Law (Definition or Statement)

In the time of 1820, there were two great French physicists Jean Baptiste Biote and Felix Savart.  after many experiments and mathematical calculations, both scientists conclude a law that was used to calculate the magnetic flux density at a given point due to the current carrying wire. Biot Savart’s law is a physical equation that tells about the magnetic field produced by a segment of wire that carries the current the segment of the wire is considered as the better quantity and is also called the current element.

It is the fundamental law of the magnetic effect of current. this law is consistent with the Gauss Theorem and ampere circuital law. We know that the coulombs law in electrostatic is a fundamental law. In the same way, the Biot-Savart law is the fundamental law in magnetism or magnetostatics.

## The formula of Biot Savart Law

To understand the formula of Bio Savart law we have to consider a wire segment of small-length ds. This length is considered a vector quantity and the direction of the segment is along with the direction of the current flown. consider the angle θ between the length of the element and the position vector from the point p, on which we have to find the magnetic field. the formula of the magnetic field by the Biot-Savart law is given below –

|dB| = (μ0/4π) (I.ds sinθ/r2)

Here, μ0 indicates the permeability of the free space and its value is equal to the 4π × 10-7 TmA-1.

If we want to find the direction of this magnetic field then be used here Right Hand Thumb Rule. according to which the thumb indicates the direction of the current loan and the other fingers indicate the magnetic field direction so by conclusion the direction of the produced magnetic field is always perpendicular to the plane in which the element and position vector Iie.

## Biot-Savart Law Derivation

The derivation is completed in the following ways-

The produced magnetic field is directly proportional to the scalar product of the current and sin theta of the small length segment and In inverse relation to the square of the separation between the point.

dB ∝ Ids sinθ

and

dB ∝ 1/r2

After combining these we get the Biot-Savart law equation as given below –

|dB| = (μ0/4π) (I.ds sinθ/r2)

## Applications and uses of Biot-Savart Law

There are some important applications of Biot-Savart law are given below they are very important from the exam point of view so you must have learned these applications.

• This is a very important law in the field of magnetism because, with the help of this Biot-Savart law, we can calculate the magnetic field and responsiveness at a very low molecular level and atomic level also.
• This law is also used to calculate the velocity which is induced by the vertex lines in the aerodynamics theory.

## Importance of biot-Savart law

This law is very important because of the following reasons-

• This law of the magnetic effect of current can be applied to small conductors which are carrying the current.
• You can also use this to apply in the symmetrical current distribution.
• This law just looks like the Coulombs of electrostatics.

## Some Frequently Asked Questions (FAQs)

Ques. Which law of physics is analogous to the Biot-Savart law of magnetism?
Ans. Biot-Savart law in physics is analogous to Coulomb’s law in the electrostatics unit.

Ques. Can we use the Biot-Savart law in place of electric field intensity?
Ans. No, we cannot use the Biot-Savart law in place of electric field intensity because we cannot find the electric field with the help of this law.

Ques. What are the two main uses of the Biot-Savart law?
Ans. With the help of this law, you can easily calculate the magnetic field at a given point. Another important we can also calculate the velocity that is generated by vortex lines.

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## Conclusion

in today’s topic of Physics – Biot-Savart law,  they learn many things that are asked in examinations. some critical types of questions such as biot Savart law equation, biot Savart law example, biot-Savart law derivation, what is biot savart law, biot savart law integral, etc describe very well in the article. so guys you can comment your doubts and curiosity in the comment section box. we will try to reply as soon as possible.