I’ve taken enough courses in “Electricity and Magnetism” that you’d think I’d have learned this by now. Sadly, you’d be wrong. Or maybe I learned it and forgot. Anyway…
Let’s say you have a flat thin sheet of conducting material, which is sufficiently large as to be effectively infinite for the purposes of this thought experiment. Suppose you apply a uniform steadily increasing magnetic field normal to the surface of the sheet. Now, I know that there will be an induced circulating current so as to create a magnetic field in the opposite direction of the increasing applied field. But what does the flow of current actually look like? Lots of little whirls? If so, what determines the size of the individual whirls, and where the are centered? (Sorry for that word “whirls”, I’m not sure if there’s a technical term for what I’m trying to say. “Vortices”, maybe?) Or do all the little whirls add up to one big whirl? If so, what determines where it’s centered? (The sheet, as I said, is “infinite”, so it has no defined center.)
I hope this question is intelligible – if not, I can try to phrase it a different way.
Is it possible to create a magnetic field as you describe? There being no magenetic monopoles, your field lines must be closed loops, no? Going both ways through the sheet?
Well, yeah, but the region in which the field lines are going one particular way could be large relative to the area we’re looking at. Like say you hold one end of a great big bar magnet next to a great big conducting sheet, and then “zoom in” on the part of the sheet that’s right by the end of the magnet.
The problem I’m having with this one is that the magnetic field is said to uniform. That is to say it exists across the entire sheet.
If it were only local, then the current would be flowing in a loop that surrounded the area where the field passes through the sheet.
You can’t replace this with lots of little loops…say you had four such loops arrainged in a square. The middle of that square constitutes a loop with current flowing the opposite direction.
I am thoroughly unqualified to answer the main question with any degree of confidence, but having had one such Electricity and Magnetism course quite recently I can add that the term we used for the “whirls” you describe was “eddy currents.”
I agree. If the region where we’re applying the magnetic field is as large as the entire sheet, then the sheet isn’t “effectively infinite”. Remember, whenever you say that something is “very large”, you have to specify large compared to what.
[QUOTE=tim314]
… you have a flat thin sheet of conducting material, which is sufficiently large as to be effectively infinite for the purposes of this thought experiment. Suppose you apply a uniform steadily increasing magnetic field normal to the surface of the sheet. Now, I know that there will be an induced circulating current so as to create a magnetic field in the opposite direction of the increasing applied field. But what does the flow of current actually look like? Lots of little whirls? If so, what determines the size of the individual whirls, and where the are centered? (Sorry for that word “whirls”, I’m not sure if there’s a technical term for what I’m trying to say. “Vortices”, maybe?) Or do all the little whirls add up to one big whirl? If so, what determines where it’s centered? (The sheet, as I said, is “infinite”, so it has no defined center.)
[/quoteQuestion? Is this really so
I hope this question is intelligible – if not, I can try to phrase it a different way.[/QUOTE]
The conducting plane is NOT cutting any magnetic lines of force and it does NOT have any induced currents, eddy of otherwise.
Elements of Electricty and/or Physics 101.
An increasing or decreasing field is a smokescreen.
Show me if I’m wrong!
PS an E.E. just stopped by and commented, “Amen!”
Bah, I’d been deluding myself into thinking you could make the region you’re looking at small enough relative to the region of uniform field (and to the size of the sheet itself) that what’s happening out near the edges wouldn’t matter. But I’ve been deluding myself – the boundary conditions would still matter. They matter even when they’re at infinity.
OK, now this doesn’t make sense to me. Surely if there’s a changing magnetic flux through the region (which there would be if you had an increasing magnetic field) then there would be induced currents. That’s just Faraday’s Law
Now I’ll grant that what they look like would presumably depend on boundary conditions, and the situation I described where there is no boundary is probably impossible. But I don’t see how there’d be no currents.
Or did you think I meant a magnetic field parallel to the surface of the conducting plane?
NO, you did say “normal” and that means perpendicular to the conducting plane.
The “Wikipedia” article addresses the magnetic flux in CLOSED LOOPS and the electric field induced along the loop.
Infinite conductive planes and magnetic fields are theoretical figments of the immagination, not real world realities.
Incidently I worked at a location which had some really huge electromagnets with pole pieces on the order of 100 sq.ft. A copper cup was unaffected by moving around between the poles. Fill the cup with LN2 and attempt to twist it in the plane perpendicular to the poles and you could end up with a broken wrist and spilled LN2.
OK, I’m still not understanding you. Through any closed loop in the conducting plane, there’s a changing magnetic flux. So there should be an induced EMF around that loop, and thus a current. Or am I not understanding Faraday’s law?
Infinite conducting plane or simply a wire in a perpendicular magenetic field. Increase the field strength. Is there an induced current in the wire? NO! A current is induced in the wire when and only when it moves relatively to the perpendicular magnetic flux. No movemen, NO current.
A simple experiment would confirm same. Simply set up a wire connected to a galvanometer or micro-ammeter in the gap of a “C” shaped electromagnet and vary the dc current. Does the meter indicate generation of a current?
Convice yotrself …
Um… I don’t think this is correct. The only thing that a loop of wire “cares” about w.r.t. magnetic fields is the change in flux going through it, period. Whether you cause this change in flux via changing the strength of the magnetic field, moving it into a magnetic field, or moving a magnet towards it, you’ll still get an induced current in the loop.
Granted, I’ve not actually performed the experiment you propose, but I find it hard to believe that every Electrodynamics textbook I’ve ever read is wrong.
Yeah, I agree with MikeS. Changing the magnetic flux through a loop of wire induces a current, regardless of how the change is accomplished. At least, there are several textbooks sitting on my shelf that all claim this is the case. Although I don’t have an electromagnet handy to test this myself. But I’d be very surprised if the experiment you (spingears) describe didn’t produce current (so long as you make sure you have a loop of wire in the gap of the electromagnet, so you can get some flux)
I have done the experiment of just changing the field strength without moving anything, as most likely has everyone in this thread. That’s how a transformer works. The input coil has a changing current, which produces a changing magnetic field and therefore a changing flux. That changing flux then induces a current in the output coil.
Back to square one. The induced currents are eddy currents, that are random, constantly swirling, and moving about like ripples in a body of water.
Because they are random they are not measurable.
Interesting!
How and with what instruments/equipment? Actual current or overall eddy current density measurement?
BTW - I found an old and forgotten aquarium air pump. Essentially an eddy current motor and wobble/oscillator piston and cylinder. Runs about 250 rpm. Temperature of enitre unit equalizes at ~ 135-140 degF. “Marco Air Pump,” Model A, 20 w. Copper rotor is 4"dia. x 1/16" thick. Continuous duty coil is “C” shaped with poles close to rotor, with ~1/16" steel shading pieces extending to lower side of pole pieces. Rotor turns toward the shading pieces. Produces about 25 cu.in.min. which is about enough for one aquarium aereator. Weight about 7-8 pounds.
You measure eddy currents the same way that you measure any other current, by the magnetic fields they produce. This is what a metal detector does: It generates a changing magnetic field, and detects the magnetic field produced by the resulting eddy currents. Why would it be any more difficult?
