Estimating Strength of a Stars Magnetic Field

Stars have magnetic fields between about 0.001 T and 0.2 T. We can estimate the strength of a star's magnetic field using the Zeeman effect. As electrons orbit atomic nuclei they generate their own magnetic field, which can either be oriented in the direction of any external magnetic field or opposed. Differently oriented atoms have different energies  
\[\epsilon_i = - \mathbf{\mu}_i \cdot \mathbf{B}\]
  and the relative probabilities of identical atoms occupying the different states is  
\[\frac{N_i}{N_j} =\frac{e^{- \epsilon_i /kT}}{e^{- \epsilon_j /kT}}\]
, and this will be mirrored in the strength of emission absorption lines in the spectrum of the star.

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