what is the relation between between the current and the magnetic moment of a current carrying circular loop ? use this expression derive the relation between the magnetic moment of an electron moving in a circle and its related angular momentum?

The magnetic moment m of a current loop is the vector whose magnitude is equal to the area of the loop times the magnitude of the current flowing in it (m = IA) and whose direction is perpendicular to the plane in which the current flows.

If T = time period of the electron

i = -e/T

1/T = f

=> i = -ef

Magnetic dipole moment is given by

M = i×A

Taking the scalar

M = iAsin(π/2)

=> M = iA

=> M = -efA