Consider a circular loop of wire of radius * a* and carrying current

*as shown in fig*

**I,***.*Let the plane of the loop be perpendicular to the plane of the paper. We going to find field

*at an axial point*

**B***at a distance of*

**P***from the centre*

**r***.*

**C**The magnetic field on the axis of a circular current loop |

Consider a current element * dl *at the top of the loop. It has an outward coming current.

If * s* be the position vector of point

*relative to the element*

**P***the Biot-savert law , the field at point*

**dl,***due to the current element is*

**P**dB resolved into two rectangular components.

- dBsinΦ along the axis
- dBcosΦ perpendicular to the axis

∴ The total magnetic field at the point

*in the direction***P***is***CP**Since

*and***μo***are constant, and***I***and***s***is the same for all points on the circular loop, we have***a**{∵ ∫

*dl*= circumference=2πa}If the coil consists of N turns, then

### Special Cases:

- At the axial points lying far away from the coil,
**r>>a**

- At the axial point at a distance equal to the radius of the coil
*i.e.,*we have**r=a**,