Hi I just saw something weird, it's not an exercise or a problem but I still have a question :
Let's say we have 2 electromagnets of unequal strengths X and X+Y; between them we have a ferromagnetic bar
Let's say one has south polarity and the other one north
if we change which one is stronger ex 1st is X,  2nd is X+Y than a moment after 1st is X+Y and  2nd is X
the bar will have the polarity of the stronger one for a moment, right?
ex for a moment the electromagnet with the south pole is stronger X + Y = the bar will become south pole
than we return it to its normal strength X and make the north pole electromagnet stronger X+ Y= the bar will become north pole, right?

How will such variations of the strength of the magnetic field on 1 side affect the entire device, will only the bar change its polarity and it will stop somewhere on the border of the second magnet or will the second electromagnet change it's polarity too if the first one's is very strong?
(just wondering) If we fix a coil on the ferromagnetic bar will such variations in the magnetic polarities of the bar induce current in it and how much, as much as we used to produce the fields of both electromagnets or only for the field of the stronger one, or only the difference between 2?
and the last question in the terms of relation between the strengths of both electromagnets (let's say in %) how much Y should be to change the polarity of the bar without affecting the polarity of the second electromagnet?
:)

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## Discussions

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I think what you are describing can be modeled as a magnetic circuit,

http://en.wikipedia.org/wiki/Magnetic_circuit

and the rules for that game are analogous the rules for modeling electric circuits.

So if you're used to Ohm's law, and simple electric circuits made from voltage sources, and resistors and stuff, then the leap to simple magnetic circuits should be pretty easy.

The magnetic analog of Ohm's law (V= I*R, where V=voltage, I=current, R=resistance) looks like:

N*I = F = Phi*R

where N*I is basically an electromagnet with N turns, and current I in each turn. This is also called magnetomotive force (MMF). It is the thing that is forcing, or causing, magnetic flux to flow. Phi is magnetic flux. R is magnetic reluctance.

Usually this R is written in fancy script, and called "script-R". Also Phi is usually the capital Greek letter Phi. This convention is followed in the Wikipedia article linked above. I would follow it here too, if I knew a way to make this editor do Greek letters and fancy script letters.

Anyway, continuing with this analogy, your electromagnets are like voltage sources (or rather MMF sources) and your ferromagnetic bar is like a resistor (or rather a reluctor, a lumped reluctance).

From your description I gather that you've got your two electromagnets pushing against each other, so that when they are of equal MMF, the flux in the bar is zero. When the electromagents are of unequal strength the flux in the bar is nonzero, and it basically gets pushed in the direction of the weaker electromagnet. Amirite?

I mean if it were two voltage sources, V1, V2, pushing against each other, connected through a resistor, R, then the current in R would be I=(V1-V2)/R

For your magnetic circuit I would expect the flux in the ferromagnetic bar to be

Phi = (F1 -F2)/R = (N1*I1 - N2*I2)/R, where the R in this equation is the reluctance of the bar.

By the way, does your question happen to be related to US Patent number

6362718?

http://www.freepatentsonline.com/6362718.html

Because, I dunno, it kind of reminds of that one. And I have no idea whether that invention actually works or not. Probably the only way to know for sure would be to build one.

Well, it has electrical inputs and electrical outputs. A naive analysis, based on conservation of energy, would lead me to believe that it produces less electrical energy than it consumes.

But that would be boring, right?

The story behind this invention, is basically that its inventor, Tom Bearden,

http://peswiki.com/index.php/Directory:Tom_Bearden

is one of these people who says it is possible to build a machine that extracts free, usable, energy from the vacuum of space itself, and I think this invention is supposed to be an example of such a machine.

I am glad I could help. Also I think there might exist free software tools for simulating magnetic fields,