How Do You Calculate Forces when The Lorentz Force Doesn't Seem to Apply?

[Keasy]

TL;DR Summary

If you place a wire with a steady current perpendicular to a uniform magnetic field, the force on the wire can be calculated from the Lorentz force equation. But if you put a cylindrical magnetic ferrite (magnetically "soft", high mu) with a center hole, over a length of the wire the unifrom magmetic field is blocked by the ferrite, and forces on that section of wire cannot be determined by the Lorentz equation.

If the mu of the ferrite is high, as suggested, the B field on that section of wire is zero, and therefore there is no force on the wire. Instead there is a comparable force on the ferrite itself. But suppose you allow the ferrite to have different values of mu. If mu=1 the force is just the Lorentz force on the wire, and for mu very large there is no force on the wire, but a significant force on the ferrite.

In the latter case, is the force on the ferrite equal to the Lorentz force normally acting on the wire? And for moderate values of magnetic permeability mu, how is the force divided between the wire and ferrite?

This looks like a problem that may have been addressed in a text somewhere, but I haven't seen it.

 

[anuttarasammyak]

I have a question about setting. Does a cylinder magnet not only shield magnetic field but also generate magnetic field that would work on wire ? Instead how about cover the wire with thin iron plates or box so that only shielding takes place ?

 

[Keasy]

The ferrite cylinder in a uniform field does generate a field that acts on the wire. If it were a clyindrical magnet with a hole I'm not sure what the forces would be, if any, with a current through the wire. I've tried iron plates and an iron cylinder rather than a cylindrical ferrite. It seems there is always an induced field and and similar forces are measured.

 

[anuttarasammyak]

Thanks.
I am not confident about the setting, but, if there is no magnetic field on the wire in your setting, no Lorentz force would be resulted. No force is ridiculous and makes any contradiction ?

 

[hutchphd]

Summary:: If you place a wire with a steady current perpendicular to a uniform magnetic field, the force on the wire can be calculated from the Lorentz force equation. But if you put a cylindrical magnetic ferrite (magnetically "soft", high mu) with a center hole, over a length of the wire the unifrom magmetic field is blocked by the ferrite, and forces on that section of wire cannot be determined by the Lorentz equation.

If the mu of the ferrite is high, as suggested, the B field on that section of wire is zero, and therefore there is no force on the wire. Instead there is a comparable force on the ferrite itself. But suppose you allow the ferrite to have different values of mu. If mu=1 the force is just the Lorentz force on the wire, and for mu very large there is no force on the wire, but a significant force on the ferrite.

In the latter case, is the force on the ferrite equal to the Lorentz force normally acting on the wire? And for moderate values of magnetic permeability mu, how is the force divided between the wire and ferrite?

This looks like a problem that may have been addressed in a text somewhere, but I haven't seen it.

.

A ferrite bead does not "shield" a static magnetic field.
The force on a ferrite bead in a uniform static external field is zero.
The force on the wire will not be changed by the presence of the bead.
Ferrite is of practically use only for AC fields. .

 

[Keasy]

Thanks.
I am not confident about the setting, but, if there is no magnetic field on the wire in your setting, no Lorentz force would be resulted. No force is ridiculous and makes any contradiction ?

Yes, there is no Lorentz force on the section of wire inside the ferrite cylinder, but there is instead a force on the cylinder. How this force is related to the Lorentz force equation is , to me, quite unclear.

 

[hutchphd]

Yes, there is no Lorentz force on the section of wire inside the ferrite cylinder, but there is instead a force on the cylinder

Why do you think this is true? Is there a reference? Data?

 

[Keasy]

.

A ferrite bead does not "shield" a static magnetic field.
The force on a ferrite bead in a uniform static external field is zero.
The force on the wire will not be changed by the presence of the bead.
Ferrite is of practically use only for AC fields. .

Ferrite material (high permeability, low magnetizability) comes in various shapes. I am using a cylinder about 3/4" dia x 1.5" long with a 1/4" hole through it, and the wire mentioned goes through the hole.. The cylinder seems to shield the wire completely from the constant field originally present. So there is no force on the wire, but instead a force on the ferrite.

 

[hutchphd]

Do you have data...like before and after introducing ferrite ?

 

[Keasy]

Yes, I've run this experiment many times, with various sized cylinders, different "uniform" magnetic field sources, and different DC currents in the wire. The results have been as described. Before introducing the ferrite I measure the field. With the ferrite in place I measure the force on the ferrite with increases in current.

 

[anuttarasammyak]

Let me share some details. Direction of magnetization of ferrite and direction of original uniform magnetic field coincide ? Direction (and magnitude also?) of force on ferrite and force on wire in original setting coincide ?

 

[hutchphd]

Please describe how you supply the "uniform" external field of that size? (2"x2"x1" is pretty large for a strong uniform field.) A piece of ferrite will experience only torque in a uniform static magnetic field.

 

[Keasy]

I create a "uniform" magnetic field over a small volume with two 4 x 6 x 1 inch magnets. I have used other somewhat smaller sizes also. Over the volume of interest the field is approximately 50 gauss plus or minus about 2 to 4 gauss.

 

[Keasy]

Let me share some details. Direction of magnetization of ferrite and direction of original uniform magnetic field coincide ? Direction (and magnitude also?) of force on ferrite and force on wire in original setting coincide ?

When I mathematically subtract the original uniform field from the total (vector) field the result is a varying field that is close to what you would expect from the ferrite itself if it were an isolated magnet.
The force direction on the ferrite coincides with what theory predicts for the wire itself. The magnitude of the original force on the wire cannot be measured very well, but the magnitude of the force on the ferrite is approximately what is expected by the Lorentz equation for the length of wire inside the ferrite.

 

[hutchphd]

While I do not doubt your measurements, the experimental conditions are far from ideal, and your explanation does not conform with any known electromagnetic theory. Ferrites do not "shield" DC fields and any piece of ferromagnetic material will feel a force only if there is a gradient in the local field.
You may wish to change your analysis considering those factors.

 

[Keasy]

I agree the experimental conditions are far from ideal, but the results I describe have been repeated with numerous set ups and instruments, and with a lot of checking for errors. A ferrite cylinder with a hole through it lengthwise, placed perpendicular to a uniform field, shows 0 field inside the hole, measured with several lab quality gaussmeters.
I do not have an analysis of these results; I'm just reporting my measurements. I was hoping there might be an analytical treatment out there somewhere I was unaware of.

 

[hutchphd]

Fair enough. If you find an analysis that shows the B field inside to be greatly diminished I will be surprised but also eager to see it! Good luck.

 

[anuttarasammyak]

Thanks to reply #14. I conjectured that ferrite is magnetized so that it cancel the original magnetic field near wire and the ferrite is attracted (or pulled) by outer magnetic field with that magnetization. If so the force on magnet does not depend on current of wire which could change, become zero and even reverse. Have you done experiments by changing current ?

 

[Keasy]

Yes, I have changed the current in most of the experiments. The force change on the ferrite seems to be directly proportional to the current for the currents I was using. Changing current direction changes the force direction. I would guess at very high currents the ferrite could be saturated. But I think you are right; the ferrite is magnetized so as to cancel the original magnetic field near the wire.

 

[Keasy]

Why do you think this is true? Is there a reference? Data?

I don't know why this is true; I would like to understand what is going on. I expected the ferrite cylinder to shield the wire so there would be no force on the wire, as I'm pretty sure it does. I didn't expect a force on the cylinder.

 

[anuttarasammyak]

Thanks to post #19 ! So is no force working on ferrite when wire current is zero ?
Now I conjecture magnetization of ferrite comes from at least partially the reaction to the circular magnetic field generated by wire current. Does such an idea work ?

 

[hutchphd]

I believe this is in fact the key. Need to give it a little more thought tomorrow.

 

[Keasy]

Thanks to post #19 ! So is no force working on ferrite when wire current is zero ?
Now I conjecture magnetization of ferrite comes from at least partially the reaction to the circular magnetic field generated by wire current. Does such an idea work ?

Yes, there is no force on the ferrite when the current is zero. The ferrite is just in a uniform field. I agree the circular magnetic field from the wire in the current must be at least partially responsible for the forces we see on the ferrite. But deriving a quantitative relationship to explain the force is more elusive.

 

[hutchphd]

Oh I see it: The total magnetic field in the presence of the current carrying wire is no longer uniform. The polarizable material (ferrite) will be drawn towards the region of higher field density which will be in the appropriate (Lorenz force) direction. Nice.

 

[alan123hk]

Yes, there is no force on the ferrite when the current is zero. The ferrite is just in a uniform field. I agree the circular magnetic field from the wire in the current must be at least partially responsible for the forces we see on the ferrite. But deriving a quantitative relationship to explain the force is more elusive

I agree that the magnetostatic problem you raised is quite complicated and difficult to obtain a complete analytical solution. Sometimes, in order to obtain accurate results, numerical solutions are inevitable.

However, I believe we can still try to reason about an abstract result of this situation based on the Lorentz force and the Biot-Savart Law.

Firstly , in an uniform magnetic field, in presence of a wire carrying electric current, and also certain ferromagnetic material, the directions of magnetic moments inside the ferromagnetic material will be redistributed in accordance to resultant effect of two magnetic fields, one is the uniform magnetic field, the other is the magnetic field generated by the wire carrying electric current.

Secondly, there will be certain magnetization current distribution appear as a result of the said redistribution of magnetic moments inside the ferromagnetic material.

Therefore, if I am not mistaken, by Lorentz force law, the force acting on that ferromagnetic material should be equal to the force acting on magnetization current inside ferromagnetic material by the total magnetic field in the space.

Again, if I make the wrong reasoning, I apologize.

 

[Dale]

Sometimes, in order to obtain accurate results, numerical solutions are inevitable.

I agree, this is a messy enough scenario that I suspect a numerical approach will be required. Also, @Keasy will need to use the macroscopic equations given in 11.10.19 here: http://web.mit.edu/6.013_book/www/book.html

 

[alan123hk]

I agree, this is a messy enough scenario that I suspect a numerical approach will be required. Also, @Keasy will need to use the macroscopic equations given in 11.10.19 here

Thank you for providing the link to the macroscopic equation in Section 11.10.19.

I think the equation can explain why the force acts on the ferrite magnet, as described in OP #1

Since an analytical solution may require a lot of mathematical work and simulation software, I am trying to infer abstract results based on the macroscopic equation by imagination.