# Magnetic Field due to Circular Current

If a coil of radius

*r*is carrying current*i*, then the magnetic field on itâ€™s axis at a distance*x*from its center is given by (Application of Biot-Savartâ€™s law; Fig. 13)**Fig. 13**

- ; where
*N*= number of turns in coil. - At center
*x*= 0 - The ratio of magnetic field at the center of circular coil and on its axis is given by
- If
*x*>>*r*â‡’*A*=*Ï€**r*^{2}= area of each turn of the coil.

# Bâ€“x curve

The variation of magnetic field due to a circular coil as the distance

*x*varies as shown in Fig. 14.**Fig. 14**

*B*varies non-linearly with distance

*x*as shown in Fig. 14 and is maximum when

*x*

^{2}= min = 0, i.e., the point is at the center of the coil and it is zero at

*x*= Â± âˆž.

# Point of inflection (*A* and *A*â€™)

Also known as points of curvature change or points of zero curvature.

- At these points
*B*varies linearly with*x*â‡’ constant â‡’ . - These are located at from the center of the coil and the magnetic field at