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Biot Savart Law - Definition, Statement, Formula, FAQs

Biot Savart Law - Definition, Statement, Formula, FAQs

Edited By Team Careers360 | Updated on May 24, 2022 09:58 AM IST

Biot Savart Law Definition.

In magnetism, Biot savart law defines the magnetic field produced at a point in space at some distance from a current carrying conductor. and This magnetic field is produced due to current flowing in the conductor.

Biot Savart Law Statement

Biot savart law states that “ magnetic field due to a current carrying conductor at a distance point is inversely proportional to the square of the distance between the conductor and point, and the magnetic field is directly proportional to the length of the conductor, current flowing in the conductor”. This is known as the biot savart law statement.

Biot Savart Law Formula

Biot Savart Law formula

Mathematically, if dl represents the small section of a long current-carrying conductor having a current of I and r is the distance between the conductor and point let’s say P and θ be the angle between dl and r so, magnetic field dB at point P due to biot savart law as shown in the diagram is given as

dB=\frac{\mu_0Idlsin\theta}{4\pi r^2}

where μ0 is known as the permeability of free space. This is the mathematical formula of the Biot savart law.

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Biot Savart law in Vector Form

The magnetic field is a vector quantity, so Biot savart law can also be written in vector form. So, if \vec dl is the vector notation of current element for in the direction of current flowing in the conductor and \vec r is the vector of the distant point so, the magnetic field at this point by biot savart law can be written in vector form as

\vec dB=\frac{\mu_0I\vec dl\times \vec r sin\theta}{4\pi r^3}

So, This is the Biot savart law in vector form.

The magnetic field on the axis of a circular current loop:


Magnetic field on the axis of a circular current loop

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The magnetic field on the axis of a circular current loop is calculated using the biot savart law and the mathematical formula to calculate magnetic field at any point on the axis of a circular loop of radius a and current carrying I, then magnetic field at a distant point P at a distance of x as shown in the diagram is given by

B=\frac{\mu_0 2\pi Ia^2}{4\pi (x^2+a^2)^{3/2}}

Magnetic field at the centre of a circular coil

Biot savart law is used to calculate the Magnetic field on the axis of a circular current loop as

B=\frac{\mu_0 2\pi Ia^2}{4\pi (x^2+a^2)^{3/2}}

so, magnetic field at the centre of a circular coil will be when axial distance x will be zero so, on putting x=0 we get, B=\frac{\mu_0 2\pi Ia^2}{4\pi (0^2+a^2)^{3/2}}

so we get,

B=\frac{\mu_0 2\pi I}{4\pi a}

Hence, magnetic field at the centre of a circular coil is

B=\frac{\mu_0 2\pi I}{4\pi a}

How to find the direction of the magnetic field in a circular loop?

If a current is flowing in a circular loop, then there will be a magnetic field produced by it according to biot savart law, so the direction of the magnetic field in circular loop is decided by using Fleming’s right hand thumb rule and it states that “curl your finger of right hand in the direction of current in circular loop, then the direction of thumb will gives you the direction of the magnetic field in a circular loop”. So, if the current is flowing in an anticlockwise direction the direction of the magnetic field will be out of the plane of the loop while in clockwise current the direction of the magnetic field is into the plane of the loop.

direction of magnetic field

(Source: Geogebra)

NCERT Physics Notes :

Biot Savart Law and Its Application

Biot savart law simply is the calculation of magnetic field due to a current carrying conductor at some distant point in space from the conductor and the biot savart law in vector form is written and calculated as

\vec dB=\frac{\mu_0I\vec dl\times \vec r sin\theta}{4\pi r^3}

Some of the most useful applications of Biot savart law are listed as:

  1. Biot savart law is used to calculate magnetic fields in space due to any current carrying conductor.

  2. Biot savart law is used to calculate the force between two long and parallel current carrying conductors.

  3. Biot savart law is used to calculate the Magnetic field on the axis of a circular current loop.

Also check-

Frequently Asked Question (FAQs)

1. State Biot savart law.

Biot savart law states that “ magnetic field due to a current carrying conductor at a distance point is inversely proportional to the square of the distance between the conductor and point, and the magnetic field is directly proportional to the length of the conductor, current flowing in the conductor”.

2. Write the Biot savart law formula.

The biot savart law formula gives the relation between magnetic field due to current carrying conductor at a distance apart. The first formula of this article explains it. 

3. What is the Magnetic field at the centre of a circular coil?

The Magnetic field at the centre of a circular coil is given in terms of permeability of free space, the radius of the coil and current through the coil. It is clearly defined in the above article

4. What is the Magnetic field on the axis of a circular current loop?

The Magnetic field on the axis of a circular current loop is calculated as mentioned in the article and can be used to find the magnetic field of the circular loop at the centre

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