We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle’s dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle’s elementary magnetic dipole moment. As consistency checks, we calculate the overall system’s energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system’s Belinfante–Rosenfeld energy–momentum tensor.

我们解决了关于经典磁力是否可以起作用的长期争论，最终肯定地回答了这个问题。详细地，我们将具有固有自旋和基本偶极矩的经典粒子耦合到电磁场，推导出洛伦兹力定律的适当推广，证明粒子的偶极矩必须与其自旋轴共线，并论证磁场对粒子的基本磁偶极矩做机械功。作为一致性检查，我们计算了整个系统的能量-动量和角动量，并表明它们的局部守恒方程导致相同的力定律，因此得出关于磁力和功的相同结论。我们还计算了系统的 Belinfante-Rosenfeld 能量-动量张量。