= Inductive impulse outside a switched solenoid
Changing the <magnetic flux> through a long <solenoid> produces an exterior azimuthal <electric field> $E_\phi(r,t)=-\dot\Phi(t)/(2\pi r)$ by <Faraday's law of induction>. A charge $q$ whose displacement is negligible during the switching receives mechanical <momentum>
$$
\Delta\mathbf p=-\frac{q\,\Delta\Phi}{2\pi r}\hat{\boldsymbol\phi}.
$$
The result assumes the usual quasistatic field approximation and neglects the particle's displacement while the pulse acts. It describes an <electromagnetic induction> effect, distinct from the static <Aharonov-Bohm effect>.
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