I'm sure I'm ascribing an incorrect visualization to the phenomena, but my image of a magnetic pole is that of a motion in liquid - like a propeller in water - ...
Just to add my two cents, I visualize a magnetic field as three superimposed scalar fields of potential energy.
Classically, potential energy is the integral of force with respect to distance or, equivalently, force is the derivative of potential energy with respect to distance. To use slightly more sophisticated language, force is the gradient of the potential. In three dimensions, imagine a room with hot spots and cold spots. The temperature would correspond to the (scalar) potential energy (field) and arrows indicating changes from hot to cold would correspond to the (vector) force field.
Anyway, an electric field is a force field (rather than a potential (energy) field). The vectors of an electric field give the force on a test charge.
In contrast, a magnetic field is (the superposition of) three potential (energy) fields. Essentially, the orientation of the test magnetic dipole selects which of the three potential energy fields the dipole is interacting with. Further, to rotate the magnetic dipole requires exactly as much energy as the difference between the potential energy fields that are selected.
So, anyway once the orientation of the magnetic dipole has selected a particular combination of the three potential fields to interact with, the translational (as opposed to rotational) force on the dipole will actually be a combination of the gradients of those three potential fields.
To summarize, electric fields give the force on a test particle while a magnetic fields give the (potential) energy of a test particle.