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Designing a Solenoid (Total Length of Wire)

Patrick Ford
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Hey, guys. So let's check out this example. So here you're you're tasked with designing a solid annoyed that produces a magnetic fields of this strength here. So B equals 0.3 Tesla at its center with a radius of four centimeters. So the radios is 0.4 m in a length of 30 or 50 centimeters or five meters, and we wanna know what is the minimum total length of 12 AMP. Wire. 12 AMP wire means that this wire is capable. Can can withstand currents of 12 amps or more. If you try. Ah, higher current. It's just probably gonna burn the wire or it's risky. What that means is that we're gonna use a I currents of 12 amps, and I want to know the minimum total length you should buy to construct this Illinois. So imagine going to the wire store and you gotta buy some some wire. How much total length Now remember, total length is different from length. Right length is just if you make a solid noi that looks something like this. This is length here, sort of like the side to side length, but the total length of wire is all these sir conferences here? Right, It's all of this. One way to think about this is if you get that solenoid that's all curled up and you pull all the way straight so that it doesn't doesn't curl anymore. What is a total length of wire you're gonna get if you did that. Okay. L is this which is given to us, but we wanna know total length, Total length. So I'm just gonna write total wire equals question Mark. And you may remember the equation for this, um, one circumference is two pi r right. Two pi r where r is the radius and were given that. But if you have any loops than the total wire is two pi r times and okay, so that's another equation that you need to know. Andi, that's what we're looking for here. Notice that I have are so that's good. And to empire constant. So that's good. But I don't have end. So before I can solve for this, I'm gonna have to calculate end and to find end. There's really only one of the equation that I can use, which is the magnetic field equation I'm given the magnetic field. So we might want to write the magnetic field equation. Be for a so annoyed is remember, Mu not I l over in. Whoops. It's actually end over. L don't get it twisted and over l or m you nuts? I little n because little n is and big and over l Okay, this is number of this is turns part meter. Okay, Just as a reminder. Cool. So I can I can find and using this equation very straightforward. So let's move some stuff out of the way and is gonna be bl divided by new knots high bl develop immunity. I b is 0. mu knots. Is four pi times 10 to the negative seven. And I is 12 amps. Okay. And if you do this, you get that end is 995 which some people would around that to 1000. But let's just say 995 turns or loops. Right? So there's 995 little winnings, and now we can plug this end into here so that the total wire is two pi The radius 0.4 and then end is 9 95. And this gives you this rounds toe Basically m of wire. Okay, so that's it for this one. Hopefully make sense. Let's get going.