Solenoids are a configuration of wires wrapped in a mass of loops that creates a magnetic field in a given direction which is used as the basis for electromagnets, or temporary electricity driven magnets.
So let's talk about Solenoids and Electromagnets. These things are very very very useful because they allow us to make magnets that we can turn on and off and we can change the strength up just by using electricity. Alright so it follows basically from ampere's law the idea is that when I've got a current loop going round like that's going to generate a magnetic field. Remember, you take your hand your right hand you put your thumb in the direction of the current and your fingers indicate the magnetic field so that means that the magnetic field in this case is coming out of the board inside the wire and into the board outside the wire so then the question is, can I make this a really strong magnetic field? That'd be great, unfortunately munot is a none expression and if you remember munot is 4 pi times 10 to the minus 7 Tesla meters per amp so that's kind of bad kind of difficult for us to cancel out 7 tens using current because even a current of 10 amps is a really big current and we don't it's kind of dangerous so, how can we use this to make our good strong magnetic field? Well what if we get a lot of these loops? If we get a lot of these loops basically just by wrapping the wire around again and again and again and again and again almost like a slinky each one of these wraps will generate a magnetic field and they'll all add together so that will allow us to get a nice strong magnetic field, such a configuration is called a solenoid, solenoid and the magnetic field inside of this solenoid is given by munot, there's that guy again, but now we've got n, n is the number of turns of wire per unit length and then times the current so let's see what one of these things looks like, so this is a picture of a solenoid here and as you can see if you do it right you can get a lot of tons per unit length and so that means that you really can make a nice strong electromagnet just from using a current in a wire.
Now generally speaking what people will do is they'll take a nice soft Ferro magnet like some iron and they'll put it in between and then that will multiply the magnetic field that they're generating by a very large amount so we can actually get nice large very strong magnetic fields that we can turn on and off and make stronger or weaker alright so let's go back over here and talk about the theory behind this so if I take this solenoid and it's coming around like this out in out in out in out in and I try to figure out the magnetic field well look my thumb in the direction of the current my fingers pointed in the direction of the magnetic field so the magnetic field in the middle of this solenoid or electromagnet is heading down. Now it turns out that if you've got a nicely formed solenoid this magnetic field will be essentially constant inside of the solenoid so all you need to do is take the solenoid put whatever you want apply the magnet to here and you got it! These things are used in junkyards for example if I want to take a car and put pick it up from one side of the junkyard put it on another side, I don't want to use a permanent magnet even I could if I could find one that's strong enough, I mean jeez if it's strong enough to lift a car, how I'm I going to get it off the thing and I put it where I want it to go? But with an electromagnet I turn it off no more current, no more magnetic fields I'm ready to pick up the next car.
Alright, now there's one other type well there's pretty more but there's one other major type of electromagnet and this is a toroidal electromagnet. Now the only difference is rather than just stacking up the loops like that what we're going to do is we're going to wrap them around in a torois in a doughnut so now we're going out in out in but we're just kind of coming around as we do it. Alright so in this case we've got a magnetic field again I'm going to grab the interior wire with my right hand pointing my thumb in the direction of the current which is out of the board and so it gives me a magnetic field that looks like this alright now the big difference here is that there's no exterior see in the solenoidal case there was an exterior here there's kind of no way to access this magnetic field but it's still very useful if I want to do something just something that's contained inside of here and I want to apply a magnetic field to it so people are using this type of design to try to investigate whether or not we can get fusion engines, well that'd be cool, the magnetic field in a toroidal electromagnet is given by this expression munot times the total number of turns times the current divided by 2 pi times the distance from the center so this magnetic field actually is not uniform in the solenoidal case it's uniform it's the same throughout but in the toroidal case it's larger near the interior or radius than it is near to the exterior and that's solenoid and electromagnets.