Question

write the expression for the equivalent magnetic moment of a planer current loop of areaA having N turns and carrying a current.use the expression to find the magnetic dipole moment of a resolving electron​

Answer 1

For equivalent magnetic moment of plane current loop of area A, having N-turns and carrying a current is,  m= ANi

For a revolving electron the equation is,

m= N(evr/2)

Image is provided below for more conceptual clearance.

Answer 2

Magnetic moment of planer current loop is M=NiA

Magnetic dipole moment -

i=e/t (q=e for an electron)

t=2pi ×r /v..... (circumference /speed)

From above 2 equations-

i=ev/2pi×r

Now,M=iA

Putting the latest value of i in above equation-

M=ev/2pi.r ×pi×r×r... (since A=pi×r^2)

On solving M=evr/2pipipi

All the best !!