We study the interaction of an electrically charged component of the dark matter with a magnetized galactic interstellar medium (ISM) of (rotating) spiral galaxies. For the observed ordered component of the field, $Bsim mu$G, we find that the accumulated Lorentz interactions between the charged particles and the ISM will extract an order unity fraction of the disk angular momentum over the few Gyr Galactic lifetime unless $q/e lesssim 10^{-13pm 1},m,c^2/$ GeV if all the dark matter is charged. The bound is weakened by factor $f_{rm qdm}^{-1/2}$ if only a mass fraction $f_{rm qdm}gtrsim0.13$ of the dark matter is charged. Here $q$ and $m$ are the dark matter particle mass and charge. If $f_{rm qdm}approx1$ this bound excludes charged dark matter produced via the freeze-in mechanism for $m lesssim$ TeV/$c^2$. This bound on $q/m$, obtained from Milky Way parameters, is rough and not based on any precise empirical test. However this bound is extremely strong and should motivate further work to better model the interaction of charged dark matter with ordered and disordered magnetic fields in galaxies and clusters of galaxies; to develop precise tests for the presence of charged dark matter based on better estimates of angular momentum exchange; and also to better understand how charged dark matter might modify the growth of magnetic fields, and the formation and interaction histories of galaxies, galaxy groups, and clusters.
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