We all want a hoverboard. We all know that it may or may not be theoretically possible to make one. And most of all we think that no decently working hoverboard will be made before the end of our lives. I don't think I'm going to change that. But I do know (at least theoretically) how a hoverboard could work which doesn't require some ridiculously big and noisy motor, nor requires a magnetic track in the road. At least, not one that isn't already there. I have thought up a concept of a hoverboard which harnesses the magnetic field of the earth to generate an uplifting force. The title image demonstrates how it works:
A current is sent through a loop, which I will assume rectangular for the simplicity of this explanation. This loop is aligned with the earth's magnetic field, such that it will exert a Lorentz force on all four pieces of the loop. Assuming that the earth's magnetic field is the same at all points on the loop, the Lorentz forces on the four segments will cancel each other.
Now, depending on the direction of the earth's magnetic field and the current, a magnetic shielding material is put around either the top or bottom part. This will (hopefully) decrease the magnetic field that piece of the loop experiences, and thereby the Lorentz force exerted on it. So this downward force is now smaller, while the upward force on another part of the loop is still as big as it was before. As a result there will be a net uplifting force. To increase this force, the current loop can simply be replaced by a coil consisting of many near-identical current loops (windings). If we can somehow make the net uplifting force bigger than the gravitational force pulling the hoverboard (and the human it's carrying) down, we have a working hoverboard! Ok, it also needs propulsion and steering mechanisms, but if we can get the thing to hover then propulsion and steering will be a piece of cake.
There are, of course, some catches. First of all, I do not know if there is any magnetic shielding material which works for magnetic fields as small as the earth's magnetic field. Heck, I'm not even sure that magnetic shielding really works the way I imagine it, so maybe the downward Lorentz force isn't reduced by it at all. Secondly, because this magnetic field is so small, it is hard to generate a big force: I have estimated that when the length of the loop is about the width of a skateboard and the wire can carry no more than a few amperes of current, something on the order of a billion coil windings will be needed to lift a human. Even with state-of-the-art nanotechnology it will be very hard to make so many windings and have their total width less than the length of a skateboard. Of course the wires could be stacked, but that can only be done like 10 times before the whole board becomes all bulky.
Luckily, scientists are already looking for something which will most definitely be a solution to this problem: (room-temperature) superconductivity. It's likely already feasible to make a working proof-of-concept with superconductors which have to be cooled with liquid nitrogen. I'm not 100% sure about this because superconductors have a "critical current"; if a higher current is sent through them they will stop superconducting, and I don't really know the typical order of magnitude of this critical current (or rather the critical current density) for common superconductors. But to me it seems plausible that room-temperature superconductivity will make my hoverboard idea feasible.
Then there is the third (and possibly worst) catch: anything interacting with the earth's magnetic field in some way may also affect that magnetic field and the mechanisms that cause it (in particular the rotation of the earth). Now, I'm not an expert on the earth's magnetic field, so some things I say about it may be overly simplistic or even wrong, but I still tried to figure out how a hoverboard will affect the earth's magnetic field. For my analysis I considered the magnetic field from the hoverboard and any forces this field may exert on the giant magnet that is the earth. I found that this field will not weaken the earth's magnetic field. It will however exert a torque on this field, which means the direction of this field will change; in fact this direction will rotate. What's disturbing about this is that this direction is related to the axis of rotation of the earth (I think), so it seems likely that this axis of rotation will also change.
After what I estimate to be a few decades/centuries/millennia we may have a situation where the rotation of the earth around its axis occurs in such a direction that half of the earth is always facing the sun (always day, possibly leading to extreme heat) and the other half has an everlasting night with an extremely cold climate. Since the rotation of this rotation axis will be slow (I don't know how slow, but as said earlier I estimate its period* might range from decades to millennia) this situation will probably last long and be very problematic. Though this likely also means that it will be a long time before this situation occurs and that we will not live to suffer it, I think we should not be blind for the impact it could have on future generations. But, as I said, I'm not an expert of the earth's magnetic field. Also I find magnetism a particularly tedious subject to analyze. As a result I may be wrong about some things, and reality might either be worse than or not as bad as it would be according to my analysis.
Likely, however, the problem can be solved by making two variations on the hoverboard in equal quantities: one which has the upper half of each coil winding shielded and one which has the lower half shielded. This way half of the hoverboards will exert a torque in one direction and the other half will exert a torque in the other direction. If they're both equally much used, they will cancel each other's torque; in practice this will not be exactly the case but still by good approximation, leading to a significant slowdown of the net effect. Also, when a net effect becomes noticeable, we can see which of the variations dominates in terms of this effect and produce less of that variation and more of the other to rotate the earth's axis of rotation back to its original position. So So with proper planning this issue does not have to be problemetic.
So there you have it, a hoverboard concept which will likely be feasible sometime in the future, with side-effects which can probably be eliminated by proper planning. Feel free to do with this information whatever you want; I'm not gonna patent this idea so feel free to use it. If you manage to mass produce hoverboards based on my idea and turn it into a commercial success, I would appreciate (but not require) some credits. I don't desire any share of your monetary profits, except of course in the form of a free hoverboard ;)
Also, if any of you knows more about magnetism and particularly about the earth's magnetic field than I do, please share your own analysis about how a hoverboard like this will affect the earth's magnetic field and axis of rotation. (Don't forget to consider the possibility that sometime in the future all 7 billion people in the world may have and use one of these things at the same time, potentially making some negligible effects less negligible.) If it does not turn out to be worse than I thought, I might just try to make a working proof of concept! Though, I will not have it lift a human, making something that can lift its own weight will probably be challenging enough.
* The attentive reader may have noticed that my first estimation was of what is actually a quarter period, but since this is a very rough order-of-magnitude estimation that doesn't really matter.