# I A strong field from a wire placed in an exterior B

1. Apr 1, 2016

### PhiowPhi

When a current carrying wire is placed in an exterior magnetic field, it's known that there is a Lorentz force, and when calculating the magnitude of the Lorentz force, the magnetic field of the wire is never considered. What if the wire's magnetic field is stronger by a huge factor to the exterior field? What effect could arise from this?

Consider the source of the exterior magnetic field to have a ferromagnetic material(whether a magnet/electromagnet), could the strong field form the wire change the magnetization of the magnet/core and reduce the exterior field applied to the wire hence reducing the Lorentz force?

Also, could there be another force aside from the Lorentz force that's magnetic?An attraction between the wire and the magnet/core's ferromagnetic material?

Assume this diagram, where the $B_W$ > $B$​

2. Apr 1, 2016

### BiGyElLoWhAt

I suppose you could. In this case, you would have a differential equation to solve.

You could treat the density of dipoles as continuous, to get a good approximation. So you have the force on the wire as a function of the field from the magnets which is a function of the field from the wire.

If the wire is infinite, then the field it produces is $\vec{B_W} = \frac{\mu_0 I}{2\pi r} \hat{I}\times\hat{r}$ and the torque on the electrons from this field is $\vec{m} \times \vec{B_W}$ where m is the moment of the individual charges. This is going to be strongest near the center, and weakest near the edges of the magnets.
This is gradually getting rougher by the minute...
Since it's ferromagnetic, I wouldn't think that assuming the individual dipoles within the magnet act independently of each other, so you'll have to take into account the dipole-dipole interactions.
Yea, it get's reeaalllyy hairy.
https://en.wikipedia.org/wiki/Magnetic_dipole–dipole_interaction
For the dipole dipoles.
https://en.wikipedia.org/wiki/Magnetic_moment
For the field-dipole interactions
I'm gonna go ahead and try to come up with a relationship for this dynamic situation, but this is as much an assignment for me as it is you. (I know not homework, but still)

3. Apr 1, 2016

### PhiowPhi

Yeah, I started to imagine the situation... and lost myself with the possibilities.
I mean, depending on the amount of time for the magnetic field of the wire to reach a steady state(which is fast considering low resistance and inductance), the field will start to change the moments of the ferromagnetic domains of the magnet(or core if it was an electromagnet) and possibly weakening the applied magnetic field and the Lorentz force, but not so sure... that's just my intuitive thought process, but what if the Lorentz force acting on the wire is "quicker" than the time it would take for the domains to change, or possibly simultaneous... confusing matter really.

4. Apr 1, 2016

### BiGyElLoWhAt

Confusing, but probably pretty fun.

So since $c_{medium}^2 = \frac{1}{\mu_{medium}\epsilon_{medium}}$, the actual rate of information change will be different, and significant on a large enough system.... (.....)
So you can imagine the domino effect on the direction of the magnetic moment of individual dipoles within a medium, from the end nearest the wire, all the way to the farthest end. It would be a domino effect at the rate of c, but a domino effect, none the less. For that to get back to the wire would then take 2 delta t, and vice versa, ad infinitum.

This is arguably the most asinine EM question I've ever seen in my life lol...

5. Apr 1, 2016

### BiGyElLoWhAt

Another thing, as far as things that don't get taken into account, EMF should be a differential equation as well, or it's at least a recursive relationship. The loop feeds back on itself, and the flux changes as a result of the current changing, which changes the flux, which changes the current, ad infinitum (=])

6. Apr 3, 2016

### Drakkith

Staff Emeritus
The lorentz force on a current carrying wire, F=ILxB, is simply a modified form of the regular lorentz force equation, F=q(E+vxB) that takes the definition of electric current into account. The force on a charged particle moving through a magnetic field is not affected by that particles own magnetic field. It is only affected by the charge of the particle, velocity through the field, and the strength of the field. Since the magnetic field of a current carrying wire is generated by moving charges, this also applies to the wire itself. A wire with a larger current will experience a larger force, not because of its own magnetic field, but because you have more charges moving, which corresponds to a larger value of q or I in the lorentz force equations.

Unfortunately I don't have an answer to your other questions. If the magnetic field is so high that it alters the magnetic properties of whatever is generating the external field then I think you should turn your magnet down!