Biot and Savart’s law can be used to find the magnetic field at the centre of a circular coil.
Let us consider a circular coil of radius ‘r’ is carrying current ‘I’ as shown in figure. Let XY=dl be the small element of the conductor. Let the element makes an angle θ = 90º with r.
Now, from Biot and Savart law, magnetic field at the centre of coil due to the element XY is given by:
Now, the total magnetic field due to the coil can be calculated by integrating from zero to 2 π. So,
If there are ‘N’ turns of coil, then:
Here the direction is B is towards the plane of the coil.