The answer is: we don't really know what causes plants to wrap one way or another around a pole. There are many theories but no scientific answers. Like people, most vines twine in a right-handed way, i.e. counterclockwise and perpendicular to the source of light, though about 10% are left-handed (clockwise) and some can go both ways. Interestingly, the right handed majority twists similarly to the right-handed rule in electromagnetism. Maybe that's where the connection with solenoids comes in. But there seems to be no scientific evidence that magnetism has anything to do with the handedness of plants. It does not have to do with north or south poles or the equator. It is genetic because some species always curl right and others always curl left. Most go counterclockwise, though.

Just as we don't know why most people are right handed, we also don't know why most plants are right (counterclockwise) twining. However, one paper speculated that, at least in roots, the microtubule structure is also right handed (counterclockwise) and that maybe because of this underlying right-handedness at the microscopic structure of plants, maybe  larger structures such as vine tendrils and stems have the same right-handedness. But basically, this is an open question: we don't know.