A changing magnetic field gradient will generate a voltage and thus a current in an electric dipole that is at right angles to the field and the gradient. An electric field will generate a current in an electric dipole.
It is not possible to have a changing magnetic field gradient without an electric field in the same place. This is embodied in Maxwell's equations. A magnetic field that affects an electric dipole will be part of an electromagnetic wave that also has an electric field that affects the dipole.