Pre-Quantum Electrodynamics

Torques and Forces on Magnetic Dipoles emsm.msm.m.fdi
  • PM 11.3
  • Gr 6.1.2

Torque on magnetic dipole:

  • Gr (6.1)

\[ {\bf N} = {\bf m} \times {\bf B} \tag{NmB}\label{NmB} \]

Tends to align magnetic dipoles with field. Accounts for paramagnetism. Exact for extended dipole in uniform field, or for point dipole in non-uniform field. Similar to electric analogue, di_N, \({\bf N} = {\bf p} \times {\bf E}\).

In a non-uniform field:

  • Gr (6.3)

\[ {\bf F} = {\boldsymbol \nabla} ({\bf m} \cdot {\bf B}) \tag{FgradmB}\label{FgradmB} \]



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Author: Jean-Sébastien Caux

Created: 2024-02-27 Tue 10:31