Assume that each iron atom has a permanent magnetic moment equal to 2 Bohr magnetons (1 Bohr magneton equals 9.27 × 10–24 A m2). The density of atoms in iron is 8.52 × 1028 atoms m–3. (a) Find the maximum magnetization I in a long cylinder of iron.

(b) Find the maximum magnetic field B on the axis inside the cylinder.


Given:


Density of atoms in iron=8.52× 1028 atoms m-3


Permanent magnetic moment (M) of each atom =2× 9.27× 10-24Am-2


Intensity of magnetization(I) is given by the formula


…(i)


Where


M=magnetic moment


V=volume


Considering volume to be 1m3


No. of atoms in this volume =8.52× 1028


Therefore, total magnetic moment=8.52× 1028× 2×9.27× 10-24Am-2



Using eqn.(i) we get



Therefore, maximum magnetization is 1.58× 10-6Am-1


The net magnetic field is given by formula



Where


I=magnetization intensity


H=magnetic field intensity


We need to find the maximum magnetic field on the axis of cylinder.


Magnetizing field intensity (H) in this case =0


Therefore



Putting the values of I and μ we get




maximum magnetic field B on the axis inside the cylinder is 2T


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