Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R.
Draw the magnetic field lines due to a circular wire carrying current I.

Here,

I = current in the loop
R= radius of the loop
X= distance between O and P
dl = conducting element of the loop

According to the Biot-Savart law,

Magnetic field at point P is,



dB has two components: dB_x and .
 is cancelled out and the x-component remains.
Therefore,



Summation of dl over the loop is given by,

B = 

Magnetic field lines due to a circular current carrying i is,