A paramagnetic crystal contains N magnetic ions which possess spin 1/2 and a magnetic dipole moment μ. The crystal is placed in a heat bath at temperature Tand a magnetic field B is applied to the crystal. Use the fact that under these conditions the Helmholtz free energy is a minimum to find the net magnetic moment of the crystal. ​

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A paramagnetic crystal contains N magnetic ions which possess spin 1/2 and a magnetic dipole moment μ. The crystal is placed in a heat bath at temperature Tand a magnetic field B is applied to the crystal. Use the fact that under these conditions the Helmholtz free energy is a minimum to find the net magnetic moment of the crystal. ​

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