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A domain in ferromagnetic iron in the fo...

A domain in ferromagnetic iron in the form of cube shaving `5 xx 10^(10)` atoms. If the side length of this domain is `1.5mu` and each atom has a dipole moment of `8 xx 10^(-24)Am^(2)`, then magnetisation of domain is

A

`11.8xx10^(5)Am^(-1)`

B

`1.18xx10^(5)Am^(-1)`

C

`11.8xx10^(4)Am^(-1)`

D

`1.18xx10^(5)Am^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
The volume of the cubic domain is
`V=(1.5xx10^(6)m)^(3)=3.38xx10^(-18)m^(3)=3.38xx10^(-12)cm^(3)`
Number of atoms in doamain (N)=`5xx10^(10)"atoms"`
Since each iron atoms has a dipole moment (m)
`=8xx10^(-24)Am^(2)`
`m_("max")`=total number of dipole moment for all atoms `=Nxxm`
`=5xx10^(10)xx8xx10^(-24)`
`=40xx10^(-14)=4xx10^(-13)Am^(2)`
Now the consequent magnetisation
`M_("max")=(m_("max"))/("Domain volume")=(4xx10^(-13)Am^(-2))/(3.38xx10^(-18)m^(3))`
`=1.18xx10^(5)Am^(-1)`
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