# Paramagnetism of Free Ions. Sign problem.

1. ### LagrangeEuler

341
Energy of system of magnetic dipoles is
##E_H=-\mu_0 \vec{\mu}\cdot \vec{H}=-\mu_0\mu_zH##
why sign ''-''?
and ##\mu_z=-g_J\mu_Bm##
Again why ''-'' sign ?
##z## is choosen to be quantization direction, and along that direction is applied field ##H##.

2. ### AlexCdeP

39
E=m$\bullet$B but as the material has a magnetization M and B= H+M then H must face the opposite direction to B and that explains the first negative sign I think.

3. ### M Quack

847
In a paramagnet, the magnetization of the material is parallel to the applied field. In a diamagnet it would be antiparallel (opposite).

The first "-" is there because the energy decreases when a magnetic moment is parallel to the applied field.

The second "-" does not make any sense to me.

H appears to be along the positive z direction. Then the magnetization mu_z should also be along the positive z direction, and it should be proportional to H. The magnitude of the magnetization also depends on the temperature.

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