 Say you had an iron nail, a ferromagnetic material that is not magnetized. It needs an external magnetic field of about 1 Tesla to become a permanent magnet. You have a power pack that runs a current of 1 amp through 600 loops of wire. What's the furthest distance you can place the iron such that it will be magnetized? The magnetic field is stronger close to the wire. So the furthest distance would be when the nail is just experiencing a magnetic field strength of 1 Tesla. We have the current, number of turns and the magnetic field strength, so we can just apply the formula to solve for distance. The magnetic field strength equals the number of wires times mu naught times the strength of the current divided by 2 pi times the distance. So putting in the numbers, we get 1 equals 600 times 4 pi times 10 to the negative 7 times the current of 1 amp divided by 2 pi r. The pi's cancel and there's also a factor of 2, so we get 1 equals 600 times 2 times 10 to the negative 7 divided by r. And rearranging, we get that r equals that, which comes out to be 1.2 times 10 to the negative 4 meters. That's 0.12 centimeters. Now just double-checking the maths by plugging everything into a calculator again. Everything checks out until you get to this point. 1 meter equals 100 centimeters, so that should be 1.2 times 10 to the negative 2 centimeters, which equals 0.012 centimeters. Well that's an unfeasibly small number. This is a solenoid. We'll be learning about them next. But it has a stronger magnetic field than just a wire. And here I have a very small nail. Smaller chunks of iron are easier to magnetize than big ones. So moving this compass around the nail, you can see no movement in the needle, and so the nail is not magnetized. If I run a current of 1 amp through the solenoid and put it next to the nail, we can try to magnetize the nail. Turning off the current, we now see the compass moving as I move it around the nail. So we've successfully magnetized a ferromagnetic material. And since it has a permanent magnetic field, even though I removed the external field, this is hard iron. An interesting thing to note here is that experiments tells us that you need a really big magnetic field to magnetize ferromagnetic materials, about 1 tesla. So how do natural magnets occur? No one is entirely sure how natural magnets came about. But one thing we do know is that they are only found on the surface of the earth, and not at great depths. The theory that fits with this observation is that the material is magnetized by lightning strikes. Lightning has huge amounts of current, on average about 30,000 amps. This will generate a huge magnetic field that's more than enough to magnetize ferromagnetic materials.