  Many extensions of the Standard Model require the existence of a "hidden"
sector. We consider settings where the hidden sector in the infrared contains a
U(1) gauge factor with magnetic monopoles, for instance 't Hooft-Polyakov
monopoles of an underlying non-abelian gauge group. In the presence of CP
violation these monopoles acquire an electric charge in the hidden sector due
to the Witten effect. We show that quite generally they also acquire (small)
electric charges under the visible electromagnetic gauge group. This is a
result of "magnetic mixing" which, as we show, often arises as a natural
partner of kinetic mixing. Both kinetic and magnetic mixing are naturally
induced radiatively even if the low-energy U(1)s arise from a single
non-abelian gauge group. We argue that the hidden sector monopoles can be light
and their electric minicharges could thus be testable in current and near
future low-energy experiments.
