Question

Density of iron is 7.8 g/cc and induced magnetic field in iron is 1 T. The magnetic dipole moment of each iron atom is $y\times {10}^{-24}\left(A{m}^2\right)$. Calculate y.

Answer 1

Induced magnetic field B = ${\mu }_0$M

$M=\frac{B}{{\mu }_0}$
= Magnetic moment per unit volume and Volume of one atom

$=\frac{Weightof1Molecule}{Density}\times \frac{N_A}{N_A}$

$=\frac{Molecularweight}{\rho \times N_A}...\left(1\right)$
So, Magnetic moment per atom
= M × Volume of one atom

$=\frac{B}{{\mu }_0}\times \frac{Molecularweight}{\rho N_A}$

Putting the values

$=\frac{1T}{4\pi \times {10}^{-7}}$

$\times \frac{56\times {10}^{-3}kg}{7.8\times {10}^{3}kg/m^3\times 6.023\times {10}^{23}}$

$=9.50\times {10}^{-24}A{m}^2$

Comparing this with $y\times {10}^{-24}$
Hence y = 9.50.