Magnetic Field at the Centre of a Circular Coil

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.

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