The solenoid filled with isotropic matter

We now consider the same solenoid, the volume of which is filled with some isotropic matter. We discuss only the case in which this material is homogenous and multicomponent. A magnetic moment per unit volume, m, is induced in the substance within the solenoid by the current. The net magnetic moment per unit volume is then given by 

For the system that we consider here, the vectors H, B, and m are all parallel, and scalar values could be used for these quantities. However, we continue to use the vector symbolism for clarity. 

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