Let the number of turns per unit radial width be n=r2−r1N.
Consider an elemental ring of radius r and width dr. The number of turns in this element is dN=ndr.
The magnetic moment of this elemental ring is dM=IdNA=I(r2−r1Ndr)(πr2).
Integrating from r1 to r2 to find the total magnetic moment M:
M=∫r1r2r2−r1IπNr2dr=3(r2−r1)IπN(r23−r13)
Substituting the given values: I=20×10−3 A, N=200, r1=0.03 m, and r2=0.06 m:
M=3(0.06−0.03)20×10−3×π×200((0.06)3−(0.03)3)
M=0.094π(216×10−6−27×10−6)
M=0.094π×189×10−6=4π×2100×10−6
M=84π×10−4≈84×3.14×10−4=263.76×10−4≈2.64×10−2 A.m2
Comparing with α×10−2 A.m2, we get α=2.64.
Answer: 2.64