What happens to a (moving) magnetic-dipole in an external electric-field? An electric-charge (positive) feels a force in direction of electric-field (external) . A magnetic-monopole, if existed, would experience force in direction of external magnetic-field, which, is proved by behavior magnetic-dipoles.
Something interesting happens when a moving electric-charge enters external magnetic-field, i.e., force is in direction given by vector-product (vector cross product) of velocity and field. But, does it means that a moving magnetic-dipole or -monopole will experience some type of force in external electric-field??
 A: You are essentially asking about what is known as the Aharonov-Casher effect (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.53.319), which is the electromagnetic dual of the Aharonov-Bohm effect. The simplest realization of the Aharonov-Casher effect arises, when an uncharged particle with a magnetic moment (spin) is encircling a tube of constant line charge density which generates a radial electric field. The circular motion leads to the accumulation of a quantum phase, the so-called Aharonov-Casher phase. The effect can be understood by considering the relativistic transformation of the electric field into the moving reference frame of the neutral particle. The magnetic moment experiences a magnetic field
$$ {\mathbf B} = \frac{1}{c^2}{\mathbf v}\times\mathbf{E} $$
brought about by this transformation, and changes its orientation under the influence of this field. The Aharonov-Casher phase is then given by
$$ \Delta\varphi_\mathrm{AC} = \frac{1}{\hbar c^2}\oint {\mathbf \mu}\times\mathbf{E}d\mathbf{s}, $$
where the integration is along the circular path of the magnetic moment ${\mathbf\mu}$.
There are experiments with neutrons that measure this phase by interference (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.63.380). 
