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 cube domain is
`V=(10^(-6) m)^(3)=10^(-18)m^(3)=10^(-12)cm^(3)`
Its mass is volumexx density `=7.9g cm^(-3)xx10^(-12)=7.9xx10^(-12)g`
it is given that Avagadro number (6.023xx`10^(23)`) of iron atoms have a mass of 55g. Hence, the number of atoms in the domain is
`N=(7.9xx10^(-12)xx6.0233xx10^(23))/(55)`
the maximum possible dipole moment `m_("max")` is achieved for the (unrealisec) when all the atomic moments are perfectly alligned.
Thus,
`m_("max")=(8.65xx10^(10))xx(9.27xx10^(24))`
`=8.0xx10^(-13)A m^(2)`
the consequent magnetisation is
`M_("max")=m_("max")//` Domain volume
`=8.0xx10^(-113)Am^(2)//10^(-18)m^(3)`
`=8.0xx10^(5)Am^(-1)`