# Driven LRC Circuits Resonance Metal Detectors Beach Airport

Do you want to know the working of airport metal detectors or any other metal detectors. Let’s talk about them. In general, metal detectors have two coils this is one coil, and this is another coil. Inductance L1, resistor R1, capacitance C1,L2, R2, C2 and so there’s a current, I1, running through this one, a current I2 running through that one. To set up the differential equations for this system is not so easy. You get two differential equations, of course, one for this system, and one for this system. The problem but at the same time the trick is that there is a mutual inductance between the two, because when this one produces a current I2, there is a magnetic flux going through this one. That’s why we call it mutual inductance, which we have never really dealt with in any detail in 8.02, and we won’t.

But I want to mention that this differential equation here is an equation in I1, L1, R1, C1, but also contains a term N times dI2/dt and this differential equation is an equation in L2, R2, C2, I2, but also contains a term, N times dI1/dt and so now you get two coupled differential equations. It’s not just one in I1, and one in I2. It is one in I1 and I2, and it is another one in I1 and I2 and that is a pain in the neck, and it’s not easy to solve. But there are mathematicians who can do all that, and they solved that for us physicists. In any case, what is important that clearly, since you have two coils, you get two resonance frequencies, not just one, but you have two resonance frequencies.

And at least one of those resonance frequencies depends very strongly on the mutual inductance and so the system is tuned to set at one of these two resonance frequencies and now someone brings in metal. You bring in a chunk of metal and in this metal the metal will experience the magnetic field, flux changes, AC of course, always, in the metal, it will start building up eddy currents and so the eddy currents will change the magnetic coupling between these two loops and so M changes and when M changes, you go off resonance, and bingo, your alarm goes off. Clearly, and very unfortunately, this never works for plastic bombs. You must have conducting material that you bring in, so it must be a metal. These systems have very high Q, very high Q means they are extremely sensitive.

If you have very high Q, that curve is extremely narrow, and so the slightest change in M, you go off resonance, and you get your alarm and so they come in various forms, and in various applications at the airport, it is very simple. You walk through these two coils. You may not have realized that, but you simply walk through. You walk through, like, there’s one coil here, one coil there, and that’s how they detect whether you have any, uh, metal on you. The one the metal detectors that are used to search your body, including the ones that are used to search the ground for coins uh, when I was a kid, I went often to the beach in the Netherlands, and there were often people who were having these metal detectors, they were looking for coins.

And those metal detectors, basically the same idea, always two coils this is this coil, and this is this coil, and when metal comes nearby, you have a system that goes off resonance, you get a difference magnetic coupling between the two coils, and the system goes into alarm and I’d like to demonstrate that, for which I need a student any student who wants to volunteer, I have here a metal detector, and, thank goodness, we don’t have to go through metal detectors yet, at MIT you want to volunteer? Boy, you’re brave, you’re all the way at the end of the can’t wait what you have in store for us. Oh, you look like you’re made of steel.

OK, you I hope you left all your secret weapons up there, did you? So this is a this is a metal detector, and if you opened this up here, you would see two coils, one in the center, and one near the edge and we have to I have to calibrate it first OK. Oh, you left your cigarettes out there? They they won’t record. What did you leave out there? I am just getting curious. Oh, you’re afraid they will get damaged? Oh, we hear nothing. That’s nice. Well, just a second, may have to recalibrate this. Pretty quiet. Doesn’t look like you have any metal there. I’m pr- fairly sure I turned it on. They don’t always work, do they? Marcos, you have any wisdom on that It’s working. It’s working well here. Wonder what you got there.

Are you metal is this not made of metal, all these things in here? Student: I have lots of metal on me, and I’m surprised it’s only going off at the belt buckle, it’s weird. Oh, you may be a weird person, that may be Can you turn around? Oh, that’s your watch. You’d better turn around again. Ah, there are the keys. You’re not made of steel, but you’re a great guy, thank you very much.