A domain in ferromagnetic iron is in the form of a cube of side length `10^-4m`. Estimate the number of iron atoms in the domain and the maximum possible dipole moment and magnetisation of the domain. The molecular mass of iron is `55g//"mole"`, and its density is `7*9g//cm^3`. Assume that each iron atom has a dipole moment of `9*27xx10^(-24)Am^2`.

Explanation

The volume of the cubic domain is
`V=(10^(-6) m)^(3) =10^(-12) cm^(3)`
`mass =volume ×x density =79g cm^(-3) x 10^(-12) cm^(3) = 7.9 xx 10^(-12)`g
It is given that Avagadro number `(6.023 xx 10^(23))` of iron atoms have a mass of 55 g. Hence, the number of atoms in the domain is
`N=7.9xx10^(-12)xx6.023xx10^(23)/55=8.65xx10^(10)atoms`
The maximum possible dipole moment `M_(max)` is achieved for the (unrealistic) case when all the atomic moments are perfectly aligned. Thus
`M_(max)=(8.65xx10^(10))xx(9.27xx10^(-24))=8.0xx10^(-13)Am^(2)`
The consequent magnetisation is `I_(max) =M_(mass)// Domain` volume`=8.0xx10^(5)Am^(-1)`