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.
I = Current in the loop
R = Radius of the loop
X-axis = Axis of the loop
X = Distance between O and P
dl = Conducting element of the loop
According to the Biot–Savart law, the magnetic field at P is
r2 = x2 + R2
|dl × r| = rdl (Because they are perpendicular)
dB has two components: dBx and dB⊥. dB⊥ is cancelled out and only the x-component remains.
∴ dBx= dBcos θ
Summation of dl over the loop is given by 2πR.