**Biot Savart Law** is used to determine the strength of the magnetic field at any point due to a current-carrying conductor. This law is given by two physicist Jean-Baptiste **Biot** and Felix **Savart**. Hence this law is known as Biot Savart Law. This law is of fundamental importance and can be verified experimentally.

Consider a very small element **PQ** of length ** dl** of a conductor carrying current

**. The strength of magnetic field**

*I***due to this small**

*dB***current element**at a point

**N**at a distance

**from the element is found to be depending upon quantities as under.**

*r*(1) *dB* ∝ *dl*

(2) *dB* ∝ *I*

(3) *dB* ∝ *sinθ*

where, θ is the angle betweenand

(4)

**Note:** *Current element* is a vector quantity whose magnitude is equal to the product of current and length of the small element having the direction of the flow of current.

combining (1), (2), (3) and (4), we get

where μ_{o} = absolute permeability

Therefore, we have

## Biot savart law in vector form

If we consider the length of element as , distance of **N** as displacement vector and unit vector along **MN** asthen

The resultant magnetic field at point **N** due to the whole conductor can be obtained by integrating the above equation over the whole conductor i.e.

The direction of is the same as the direction given by. The direction of can be determined by right hand thumb rule for finding the direction of the vector product of vectors. Here, at point N, the direction of is perpendicular to the plane containing andand is directed inside the plane of paper represented by the symbol **⊗ **as shown in figure 1.