# 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.

Answer

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

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

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