For x >> R, we may drop the R2 term in the denominator Thus,
2
0
3
2
IR
B
x
µ
=
Note that the area of the loop A = pR2 Thus,
0
3
2
IA
B
x
=µ
π
As earlier, we define the magnetic moment m to have a magnitude IA,
m  = I A Hence,
B
≃ µ0m
3
2 πx
    
π
0
3
2
4
x
=µ
m
[4