 In the previous case study, we had a magnetic field of less than 1 microtesla. That's actually really small for a magnetic field. If you held a compass to the wire, you probably won't be able to see a noticeable deflection. So to get a bigger magnetic field, we can do a few things. Looking at the equation, mu0 and pi are both constants, so we can't change these variables. Which means to change the strength of the magnetic field, we need to shorten the distance of the wire, or increase the current. If we reduce the distance, even to 1 cm, it won't make a huge difference till you get to the micrometer scale, which is a bit hard for everyday purposes. So that leaves us with the other option, to increase the current. Only thick wires can conduct high currents. A normal wire conducts only a few amps before it'll burn. However, creating strong magnetic fields with thick wires like those you see on telephone poles is super expensive and hard to move around. So how we normally solve this problem is to have lots of thin wires. We've previously learned that magnetic fields are vector fields. So to find the overall magnetic field, we add up the individual magnetic fields. If we had a second wire right next to this aqua one, with the current going in the same direction at the same strength, the overall magnetic field would be the sum of the magnetic field due to both wires. So let's call the magnetic field due to the aqua wire, BA, and the magnetic field due to the brown wire, BV. Then the overall magnetic field, BT, would be a sum of these two. We know how to find the magnetic field of a single current at some distance r away. B equals mu naught i divided by 2 pi r. And since both have a current going in the same direction, the right hand rule would tell us that the direction of the magnetic field would also be in the same direction. Both wires have the same amount of current running through them and are at the same distance away from our point. Then BT would equal mu naught i divided by 2 pi r plus mu naught i divided by 2 pi r, which is the same thing as doubling the magnetic field strength of one wire. Now what if we had more wires, 10, 100? If all these wires have a current going in the same direction, then they would all generate the same magnetic field, which would reinforce each other, generating an even bigger overall magnetic field. And if we apply the same analysis method, we get that the overall magnetic field is just the number of wires times the individual magnetic fields. So the magnetic field due to multiple wires is n mu naught i divided by 2 pi r, where n is the number of current carrying wires. Increasing the number of wires is both cheap and portable. Here's an example. This has 600 turns of wire. Compare the magnetic field around this to one wire. Same current, same distance, but the difference is no...