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.

Answer

`1*58xx10^6Am^-1`; `1*985T`

Explanation

Here, magnetic moment of each atom
`=1*85xx10^(-23)Am^2`
Number of atoms/volume `=8*52xx10^(28)m^-3`
`:.` Max. magnetisation,
`I=M/V=1*85xx10^(-23)xx8*52xx10^(28)`
`=1*58xx10^6Am^-1`
Max. mag. Induction `B=mu_0(H+I)`
`=4pixx10^-7(0+1*58xx10^6)=1*985T`