Lec 19 MIT 6.013 Electromagnetics and Applications, Fall 2

JAMES MELCHER: Edgerton's Boomer illustrates the induction of a current in a conductor subjected to a time-varying magnetic field and the associated magnetic forces. It illustrates the interplay between the laws of Faraday, Ampere, and Ohm that determines the distribution, duration, and magnitude of currents in conductors under magnetoquasistatic conditions. This is the coil. The winding wire circulates like so and is connected to the capacitors in this cabinet by these leads. When the high-voltage power supply in the cabinet is turned on, the capacitor is charged to 4 kilovolts. The switch then connects the capacitor to the coil. It's closed when this button is pushed. The switch consists of a spark gap, which we just heard. We can see it if we open this panel. The switch is closed by a spark across this gap. That spark is activated by applying a voltage to this electrode to make a smaller electrical breakdown in the gap. Just once, we'll bypassed the safety interlock that ordinarily disconnects the circuit when the panel is opened. Then, when we push the button, we can not only hear the spark discharge that closes the switch, but see the associated flash as well. Maybe we can do it once more. Given the initial capacitor voltage of 4 kilovolts and that the coil has 50 turns, we can use basic principles to estimate the winding current, and hence, the magnetic field intensity produced by the coil. First, we use Ampere's integral law to relate the current to the field. The line contour encloses the current in the coil. Before we go on, let's see how well we've approximated the current and field. This current probe will link one of the wires connected to the coil. We display the coil current on the lower scope trace. The voltage induced at the terminals of this coil by the time-varying magnetic flux density will be used to deduce B. This voltage will be displayed as the upper scope trace. Here are the responses to the discharge of the capacitor. The time axis is 2/10 of a millisecond per division. So the period of the oscillation is about 1/3 of a millisecond. The oscillation frequency is roughly the predicted 4 kilohertz. The duration of the lower trace current, and hence, of the field, is on the order of 1 millisecond. The peak in the current on the lower trace is about one division. There are 1,000 amps per division. So the peak current is about 1,000 amps. This is in the range of the estimated value of 1,600 amps. Remember, we've not accounted for losses in the spark gap and the coil. The disk could represent a hand. In that case, the experiment can literally give a feel for the consequence of subjecting a conductor to a time-varying magnetic field. If the disk represents a hand, what current density would be felt? The magnetic field created by the coil is non-uniform, far away that of the dipole. So we can discern what we're getting into by feeling the induced current in stages. The sensation is of a short-duration twinge, much as would be expected for a pulse that lasts 1 millisecond. I've been given to understand that Professor Zahn is not going to try it with his hand lower than this. So that you can see evidence of the field that you can't feel firsthand, let's replace his hand by this wire loop. The wire is open at this point, with the ends barely touching. So the field induced around the contour is concentrated at the gap. We go to a higher F stop to protect the camera. The integral of the electric field intensity is concentrated in a gap region that is initially relatively insulating. So the electric field intensity between the almost-touching wires is enough to produce a spark. The conductivity of this aluminum disk is more than 10 million times larger than for human flesh. And there's no gap to limit the induced current. The force can be used to shape metals. Here, the upward force is evident in the shaping of the outer edge of a foil disk. For this experiment, we used three times as much capacitance. If the force can be used to shape the metal, it can also be used to launch the disk. I'm Melcher, and as you know, that's Zahn. We brought along an illuminary here to push that button, finally. This is Professor Doc Edgerton. And it's his machine. What we've done, of course, is to show you this disk. And now, if, Doc, you turn on your machine-- DOC EDGERTON: Ready? Here we go. JAMES MELCHER: I'm going to step out of this. DOC EDGERTON: I'll turn on the main power, let it come up to charge. Woo-ee! Want to do it again? JAMES MELCHER: Do you have a favorite one there? DOC EDGERTON: Well, every one's a little different. Let's try this one. What do you say? Power. [HIGH-PITCHED RING] JAMES MELCHER: A little different ring to it. DOC EDGERTON: Little different ring. JAMES MELCHER: Now, as I understand it, this thing's got more capacitors in it. Maybe we get Zahn to put a little more in there? DOC EDGERTON: Yeah, you'd like to have it a little higher? MARKUS ZAHN: Sure. JAMES MELCHER: One of the reasons I brought this man along is that, in fact, he mainly paid for this building. So you see, we don't care too much if we hurt that ceiling. DOC EDGERTON: It'd be nice to have an imprint up there, wouldn't it? JAMES MELCHER: Right. With you here, I can say that. DOC EDGERTON: OK, let's see what happens this time. We've got three capacitors on instead of one. It should go a little higher. 1, 2, 3, go. [CLATTER] Woo-ee! Missed me. JAMES MELCHER: Want to try our favorite one? DOC EDGERTON: Yeah, let's try that one. [LOUD CLATTER] Hey! Knocked a hole in the ceiling. JAMES MELCHER: I can see you enjoy that, huh? All right. Thank you very much, sir.

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