 Now, we look for the magnetic field inside a solenoid. In this case, I want to start by describing what is a solenoid. One definition is a long wire that's wound into a helix. Can you imagine it might picture it like this? I've got wire coming in and then it loops around and around and around and around as it moves down the length of the solenoid. If you hear something called an ideal solenoid, that means two things. One, the loops are close together, meaning there's not as much of a gap like it shows here. And the overall length of the solenoid is much longer than the radius of the individual coils of the helix. So now we get to look at the B field for this. Well, if I was going to use the Bio-Sovart law, it'd be really complicated to solve by hand, but computers can do it pretty easily. Here's a simulation of what it looks like if I actually calculate the magnetic field around one of these solenoids. Now, to help you picture what's going on here, imagine each of these individual little dots represents a cross-section of my solenoid. So my wire is actually coming out of the screen here, wraps around in space, comes back in, loops back around, comes out here, et cetera, forming my loop as I'm going down the page. So this is the length of the solenoid, and this is sort of the cross-sectional radius of my solenoid. These lines here with the little arrows on them show me the magnetic field that's calculated from the Bio-Sovart law. Now I want to point out just a few things to you about what we see from this computer simulation. One, inside the solenoid, the B field is pretty much uniform. So the lines are about equally spaced, and they all point in the same direction. And the more ideal your solenoid is, the closer to uniform this is. Outside the solenoid, there's almost no B field. I say almost because there's a very, very weak one out here. Over here on the edges, that uniform field starts to diverge as it's going out. So while it's really uniform inside the solenoid, as soon as you get up towards the edge of the solenoid, you start to see those magnetic field lines spreading apart. But in general, it comes out one side, and back in the other side, and you've got a uniform magnetic field in the region in between. So what is that magnetic field inside the solenoid? Well, it turns out if we use Ampere's law, then we can derive this formula that's shown here. Again, our mu naught is our magnetic constant, our i is the current, n is the number of loops, and our l is the length of the solenoid. Some texts will put this as a capital L as just a regular letter l, some of them will show it as the lower case with it more of a cursive l. This quantity, n over l, is sometimes given as a single thing, the turns per length, or the loops per length of wire. Notice that nowhere in this equation does it refer to the radius of the solenoid. And it turns out it doesn't matter what the radius of the solenoid is. As long as you're inside a fairly ideal solenoid, the magnetic field is going to be given by this equation.