Homopolar motors and a greater understanding of Magnetism
Recently, I have been trying to gain a better understanding of how motors work. While searching the interwebs, I found a number of tutorials explaining the magnetic interactions found in motors. But many of these sites and videos failed to explain the mechanics of magnetism itself. So I dusted off my E&M book and went for it. One hour later, and my brain was fried. I had forgotten how complex Electricity and Magnetism was. Doing what any self-respecting engineer would do, I watched an unhealthy amount of YouTube. During my binge, I continued to see "Homopolar motor" and "Simplest Motor" show up. Being curious, I decided to build one and see how it worked.
As you can see, it's about as simple as it gets: a piece of wire, magnet, and a battery. Well, how does it work? Let's take a look!
Simply put, the Lorentz force is responsible for propelling the motor. To be more exact, it's how the Lorentz force acts on a current-carrying wire. The resultant force is the cross product of current (along a length "l") and the magnetic field. For our purposes, we will ignore length to keep things conceptual.
An easy way to represent the cross product is to think of the Right Hand Rule.
To re-phrase our use of the Lorentz force definition: Force is the product of current as it is orthogonal to the magnetic field. The resulting force must be orthogonal to both current and the magnetic field. What if current and the magnetic field are not perfectly perpendicular? The cross product helps us make this easy. Let's take a simple problem:
The cross product helps us take only the parts of the field as it acts on current. In my example, "B" would represent current, and "A" would represent the magnetic field. To determine the direction of the force, you always start with your thumb along the first vector (Ay), and point your fingers in the direction of the second vector (B). The force will be in the direction your palm is facing. In our case, this is "into the page." The circle with the "X" is supposed to look like arrow fletchings flying away. A arrow coming towards you, or "out of the page," would have a single point.
What if I do the same problem only with C = BxA? Well, what are you waiting for? Try it! The only difference is now your thumb goes along B and your fingers along Ay. You get the same force, but reversed. This demonstrates the importance in the order we solve things. The cross product is not what mathematicians would call commutative. Now, take our example motor diagram above and reverse the current. Following the rules of the cross product and reversing the direction of current reverses the motor! Let's take a look a one running.
The magnetic field is created by the magnet below the battery. This is shown as red field lines traveling from the north to south pole of the magnet. Current is represented by the yellow arrows as it flows through the wire (the magnet is providing the slip ring connection to the bottom of the battery). The green arrows are showing the force created by the interaction.
Well that was cool! What happens when you lay it out flat? You get a linear homopolar motor!!!
Building one is simple. You just need some form of rails, magnets, and a non-ferrous conductive rod/tube. I found that model rail track was easy to get. I grabbed a box of magnets from inventory, and the copper tube was something I found at the hardware store. Finally, I laser cut some plastic to help me hold it all together. It's important to glue all the magnets in the same orientation or the rod will not continue down the track. This can be done by marking them or checking polarity as you assemble. Special thanks to Riley H. for helping me glue all these magnets together!
What if we crank up the current? Thanks for asking! Well, for starters, things get hot. So hot that when we add say, 5 million amps, things start to turn to plasma.
The need for an external magnetic field is also removed. Passing current through a wire creates its own magnetic field. This is governed by Ampère's circuital law. We'll save that topic for a later date. Now, how is this useful? There are plans to use systems like this to put satellites into orbit without burning rocket fuel. Time will tell if it works out!
This was a great tangent I took while writing the new Motor Tutorial. I learned a lot about magnetism, and it really solidified my understanding of the subject. Check it out and see how some of these concepts are put into the context of a motor you might actually use.