  The Berry curvature, resembling the magnetic field in reciprocal space,
offers a captivating avenue for exploring unique electromagnetic phenomena
devoid of real-space analogs. Here, we investigate the emergent electromagnetic
induction by solenoidal Berry curvature with its field lines forming loops,
links, and knots. In stark contrast to Faraday's law, which dictates that
alternating magnetic fields yield alternating electric fields with a net zero
average, the alternating Berry curvature can engender directional
electromagnetic induction. Such an effect is attributed to the presence of
singularities in the Berry curvature, accompanied by a $2\pi$ jump in the Berry
flux. Notably, this jump does not trigger a diamagnetic impulse, due to the
gauge invariance of the Berry phase modulo $2\pi$. Consequently, the induced
electric field maintains finite values under time averaging, manifesting itself
as a directional pumping current. Our research sheds light on an anomalous
electromagnetic induction effect directly arising from the singular gauge
transformation, thereby expanding our comprehension of exotic electromagnetic
phenomena.
