Stupid electromagnetics question

I'm having some trouble getting my head around this:
A current flowing through a (static) conductor produces a (static)
magnetic field around it, as described by Ampere's Law.
But the reverse appears not to be true; A magnetic field around a conductor doesn't induce current to it, unless the conductor is moving or the magnetic field changes (or both.)
Isn't this a paradox?
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Paradox? No. Why should they behave the same? What is the apparent contradiction? E behaves one way, B another.
Is it an asymmetry where in a beautiful and perfect universe we might expect complete symmetry between the equations that E and B follow? Yes, it's an asymmetry. The equations don't have the same form. That's just the universe we live in.
Static charge distributions produce static E fields with nonzero divergence (for instance, everywhere radially outward) and zero curl (they can't form closed loops).
Static current distributions produce static B fields with zero divergence (no purely radial B fields) and nonzero curl. Not the same.
However, there is a deeper symmetry, in that B and E can be unified into one "electromagnetic tensor" and the four Maxwell's equations combined into one: http://simple.wikipedia.org/wiki/Maxwell 's_equations
- Randy
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But, Ampere's Law states that:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html
So if we have B around a conductor, surely we have to have I as well. That's what the Law states. I know I'm missing something, but what do I miss?
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in

One is the cause of the other. The source (the current) is the cause; the field is the effect. It isn't appropriate to switch cause and effect, any more than it is appropriate to say that just because F=ma then acceleration causes a force -- it doesn't.
Now what you *can* say is that if there is a magnetic field in a certain region of space, then there is likely a current *somewhere* that is responsible for that field. But if you just happen to put a wire in that field doesn't mean that the current responsible for the field has to live in that wire.
A simple example: Take a H-shaped transformer, something you can pick up at Radio Shack. Apply a DC current to the primary with a 9V battery in series with a reading lamp bulb (to confirm the current). This will generate a magnetic field in the transformer core, which you can confirm by putting a paper clip next to the core. However, you will register no current in the secondary, as you can confirm with another reading lamp bulb.
[Note in passing: the *correct* form of Ampere's law notes that there are two possible sources of a magnetic field: a current, and a time- dependent electric field.]
PD
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I understand it now. If there's a magnetic field somewhere then that magnetic field is *always* caused by a current. So there's no way to create the magnetic field of a current-carrying conductor without using one.
Thanks.
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in

Add the word STATIC and you're OK. Magnetic fields are induced by currents and by time-varying electric fields, but (I'm pretty sure) you can't get a static magnetic field unless there's a current somewhere.
Having said that, permanent magnetic materials throw a little monkey wrench into the theory. The source of magnetism in magnetic material is electron spin, tiny magnetic dipoles. There isn't actually a classical current, but you can *model* them as little imaginary current loops for the purpose of Maxwell's equations.
- Randy
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Permanent magnet.
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The Great Attractor

The magnetic field of a permanent magnet is caused by currents inside the body of the magnet.
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On Fri, 11 May 2007 17:51:59 +0000 (UTC), qwerty

It is caused by alignments of atoms in the lattice of the medium.
They all spin in one plane.
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: : >> you can't get a static magnetic : >>field unless there's a current somewhere. : > : > : > Permanent magnet. : > : : The magnetic field of a permanent magnet is caused by currents inside : the body of the magnet.
And you know this how?
The electrostatic field of a capacitor is caused by fluxes in the body of the capacitor, you can't get a static electric field unless there's a flux somewhere. You don't buy my theory, huh? I don't buy yours, then.
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Add up a gazillion of 'em, and get a cumulative effect we call a field.
Get a big planetoid sized orb full of iron and it will likely be magnetic to some degree. That's Gazillions to the Gazillionth power. :-]
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in

Keep in mind the weirdness that I added as a footnote. Even a changing *electric* field can produce a magnetic field. Though this may seem like a little oddball thing that doesn't happen very often, it is in fact half responsible for your being able to see anything. (Light.)
PD
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ESD damage can occur to chips due to electric fields, so yes, they DO have influence.
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in

bad PD!
http://google.com/groups?q=Autymn+are-magnetism
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On 5/10/07 12:23 PM, in article Xns992CE3D7689CFp3ifw90nsdek@193.92.150.76,

You have to think of Maxwell's equations.
Ampere's law is the equivalent of
Del X H = J + dD/dt
where J is current flow per unit area.
The corresponding equation for E is
Del X E = -dB/dt.
The derivatives should be partial derivatives.
There is no magnetic equivalent for current. That is, there are no magnetic monopoles although there are electric charge monopoles. Find magnetic monopoles and you will have a secure place in the history of science. Fortune too.
Bill -- Fermez le Bush--about two years to go.
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If they existed at all they must always have been around.
Maybe we just don't recognize them yet for what they are (if they do exist).
Andr Michaud
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I'd have brought my violin if I'd known you were going to sing.
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A waterfall makes a pool of water, but the reverse appears not to be true; a pool doesn't make a waterfall. Isn't this a paradox? :-)
What would you need to do for the pool to make a waterfall?
Answer: collect the pool in a rubber bulb and squeeze it to make a fountain, collecting the water that rose up (as you might do at a drinking fountain). A fountain is an upside down waterfall.
If you collapse the magnetic field, then you'll push the current back the other way. That is essentially what a generator does.
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Androcles wrote:

I'm pretty dumb about these things, but doesn't a collapsing magnetic field (such as around an inductor) attempt to push the current in the direction it was going when the field was created? IOW, doesn't it become EMF in the same direction as the current was flowing already?
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Anthony Fremont wrote:

Yeah you are pretty dumb, but apparently not dumb enough! :-) It's called Lenz's Law and the principle is that when you set up or tear down a magnetic field it always tends to oppose the action you are undertaking. Therefore if you are trying to put a current into an inductor (which sets up the external field) setting up that field will cause the inductor to resist the current you are trying to push through it. Similarly, if the inductor already has a current flowing, the collapsing field will try to keep the current going, namely resist your actions of trying to STOP the current. so yeah, you are correct. The basic idea is that in shoving current through an inductor you are in essence shoving energy into the magnetic field about it where it is stored. Later when you try to stop the current, all that stored energy comes back out of the field and does so in a direction that tends to keep the current flowing in spite of your efforts to stop it.
Benj
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