Assume that each iron atom has a permanent magnetic moment equal to 2 Bohr magnetons `(`1 Bohr magneton equals `9.27 xx 10^(-24) A m^2``)`. The density of atoms in iron is `8.52 xx 10^28` 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.

Explanation

For maximum possible magnetization we can assume that 100 percent atoms are aligned. Intensity of magnetization is magnetic moment per unit volume, hence we can multiply magnetic moment of each atom with number of atoms per `m^3`of sample then we get intensity of magnetization.
`I = 1.85 xx 10^(-23) xx 8.52 xx 10^28 A//m = 1.58 xx 10^6 A//m`
Maximum magnetic field at the centre of cylinder can be written as follows:
` B = mu_0 I = 4pi xx 10^(-7) xx 1.58 xx 10^6 = 2T`