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?

Reply to
qwerty
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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:

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's_equations - Randy

Reply to
Randy Poe

Randy Poe wrote in news: snipped-for-privacy@y80g2000hsf.googlegroups.com:

But, Ampere's Law states that:

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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?

Reply to
qwerty

innews: snipped-for-privacy@y80g2000hsf.googlegroups.com:

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

Reply to
PD

A waterfall makes a pool of water, but the reverse appears not to be = true; a pool doesn't make a waterfall.=20 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,=20 collecting the water that rose up (as you might do at a drinking = fountain). A fountain is an upside down waterfall.=20

If you collapse the magnetic field, then you'll push the current back the other way. That is essentially what a generator does.

Reply to
Androcles

I wouldn't call it a paradox (or a stupid question, either). The situations are not symmetric - in the first, there is a static electric field as well, producing the current.

You could say that, in the first case, the electric field driving the current produces the current and the magnetic field. You can get rid of the current in Ampere's law by substituting J = sigma E, where J is the current density and sigma is the conductivity.

Another thing that stops it from being symmetric is that the current is moving electric charge, driven by an electric field. The symmetric case would be a magnetic current, composed of moving magnetic monopoles, being driven by the magnetic field and producing a static electric field. No magnetic monopoles, so we don't observer this.

(Exercise for the reader: assume magnetic monopoles exist, and design a perpertual motion machine thereby.)

You might be interested to know that sometimes magnetic currents are assumed to exist, to simplify calculations in problems where electromagnetic waves interact with objects (ie scattering).

Reply to
Timo A. Nieminen

PD wrote in news: snipped-for-privacy@l77g2000hsb.googlegroups.com:

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.

Reply to
qwerty

I'd have brought my violin if I'd known you were going to sing.

Reply to
Androcles

innews: snipped-for-privacy@l77g2000hsb.googlegroups.com:

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

Reply to
Randy Poe

Not really.

You sort of assume that the magnetic field you visualize around the conductor suddenly appears full strength about it.

In reality, it will have to build up to full strength as it is generated by current flowing in some other nearby conductor or from the magnetostatic field of a permanent magnets being moved towards the conductor .

As this magnetic field intensifies about your conductor, current will flow in it, but will stop flowing when the magnetic field is made to stop increasing. Current will start flowing again it you start decreasing the magnetic field.

Moving current induces magnetic field.

Moving magnetic field induces current.

No paradox.

Andr=E9 Michaud

Reply to
srp

I've never heard of a photon being called a "perpetual motion machine" before, but they do seem to travel a long way.=20

Reply to
Androcles

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.

Reply to
Salmon Egg

innews: snipped-for-privacy@l77g2000hsb.googlegroups.com:

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

Reply to
PD

Yes, and AC current makes for continually moving flux. DC makes a standing field.

To INDUCE (key term here), the flux MUST be in motion. The field doesn't have to "change" as you put it. It HAS TO MOVE, as in lines of flux must "cut" through the conductor, and the current induced in it will always be varying, not static.

Nope.

Reply to
The Great Attractor

Permanent magnet.

Reply to
The Great Attractor

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. :-]

Reply to
The Great Attractor

No. whenever it stops *moving*. It doesn't have to change strength, just position.

Reply to
The Great Attractor

WOW... one kook posting to another.

Why don't you guys discuss it so we can all have a laugh?

Reply to
The Great Attractor

ESD damage can occur to chips due to electric fields, so yes, they DO have influence.

Reply to
The Great Attractor

No. The logic is faulty. It is like stipulating that "all sandboxes contain sand" and because of the stipulation assuming that "all sand is in a sandbox".

From Ampere's law you stipulate that a current through a wire results in a magnetic field around the wire. (That's the sandbox). You incorrectly assume, because of that stipulation, that a magnetic field around a wire must induce a current.

Ed

Reply to
ehsjr

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