Magnetic properties of substance

A material possesses a magnetic susceptibility of 0.00045. What are this material’s relative permeability and permeability, K and $\mu$ respectively? Find the strength of the total magnetic field in the material, B, when it is immersed in an external magnetic field of 2 T. What is the magnitude of the magnetization per unit volume of the material, M, then? Enter your answers with five significant figures, except where indicated otherwise.


By definition

relative permeability = 1 + susceptibility 

$K = 1+ \chi = 1+0.00045 =1.00045$

absolute permeability = vacuum permeability*relative permeability

$\mu = \mu_0*K = 4*\pi*10^{-7} *1.00045 =4.0018*\pi*10^{-7} =12.572*10^{-7} (H/m)$

$H$ is magnetic field strength

$B_0 = \mu_0*H$    external magnetic field
$B = \mu*H = \mu_0*K*H =k*B_0 = 1.00045*2 =2.0009 T$

$M$ is magnetization

$B = \mu_0*(H+M) = \mu_0*H + \mu_0*M = B_0 +\mu_0*M$

$M = (B-B_0)/\mu_0 = 0.0009/(4*\pi*10^{-7}) =716.197 A/m$