= Magnetic angular-momentum invariant
{title2=$\mathbf L\cdot\mathbf B+\frac q2|\mathbf r\times\mathbf B|^2$}
For a particle obeying $m\dot{\mathbf v}=q\mathbf v\times\mathbf B$ in a constant uniform <magnetic field>, the displayed combination is conserved. The derivative of mechanical <angular momentum> projected onto the field is canceled by the quadratic position term. This is the rotational analogue of the distinction between mechanical and <canonical momentum> in an electromagnetic field.
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