- #1
Keasy
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- TL;DR Summary
- If you use a permanent magnet and current-carrying wire, the Lorentz force law accurate predicts the forces between them. However, if you use an induced magnet field with a current-carrying wire, the predicted force may be accurate, or completely different from what is expected.
If you take a bar magnet and place a wire with current a short distance from the end, Lorentz's law can be used to accurately predict the location and magnitude of the resulting forces. The same is true if you use a large volume uniform magnetic field to create an induced field in a bar ferrite and consider only the field induced in the ferrite. The forces on the ferrite: location, magnitude, and direction are as expected.
However, if you change the shape of the ferrite to something that is not long in the direction of the inducing field, that is no longer true. You can measure the induced field in the ferrite at the wire location, but the resulting force on the ferrite, and its location, can be wildly different from what would be expected from Lorentz's Law.
For example, suppose you establish a uniform magnetic field and measure its magnitude, say B0. The field is horizontal. Then you take a ferrite that is thin compared to its width and length and place it on a horizontal support, say a tongue depressor. The ferrite is mounted so the short dimension is perpendicular to B0. The ferrite and support are placed in B0 near an existing wire which is perpendicular to the field and parallel to the ferrite face. The ferrite is placed so the face of the ferrite is a short (inch or so) distance from the wire. Then the ferrite is moved up or down so its face is centered on the wire.
The field at the wire is now measured and labeled BF (for final). BF - B0 is the induced field at the wire from the ferrite. Call this Bi (B induced)
Now we support the tongue depressor with two "point scales" (a scale supports and measures the vertical force at a specified horizontal point only). One is located an inch or so to the left of the ferrite, (say location S1), and the other, say S2 is located directly under the wire.
When we place a current in the wire we expect a force reading on scale S2, directly under the wire, proportional to Bi times the current magnitude. We expect S1=0. Of course, in all cases the scales are zeroed before we turn on the current. But with different geometries, as the shape of the ferrite is varied we can easily see S1=S2 , or S1 may be a significant value while S2=0. And in all cases the measured induced field Bi looks quite reasonable.
This seems quite unexpected. But these results have been measured many times with lab quality instrumentation and different hardware, including different large magnets used to set up the uniform magnetic field. And these results were obtained with several magnetic materials; it need not be a ferrite.
However, if you change the shape of the ferrite to something that is not long in the direction of the inducing field, that is no longer true. You can measure the induced field in the ferrite at the wire location, but the resulting force on the ferrite, and its location, can be wildly different from what would be expected from Lorentz's Law.
For example, suppose you establish a uniform magnetic field and measure its magnitude, say B0. The field is horizontal. Then you take a ferrite that is thin compared to its width and length and place it on a horizontal support, say a tongue depressor. The ferrite is mounted so the short dimension is perpendicular to B0. The ferrite and support are placed in B0 near an existing wire which is perpendicular to the field and parallel to the ferrite face. The ferrite is placed so the face of the ferrite is a short (inch or so) distance from the wire. Then the ferrite is moved up or down so its face is centered on the wire.
The field at the wire is now measured and labeled BF (for final). BF - B0 is the induced field at the wire from the ferrite. Call this Bi (B induced)
Now we support the tongue depressor with two "point scales" (a scale supports and measures the vertical force at a specified horizontal point only). One is located an inch or so to the left of the ferrite, (say location S1), and the other, say S2 is located directly under the wire.
When we place a current in the wire we expect a force reading on scale S2, directly under the wire, proportional to Bi times the current magnitude. We expect S1=0. Of course, in all cases the scales are zeroed before we turn on the current. But with different geometries, as the shape of the ferrite is varied we can easily see S1=S2 , or S1 may be a significant value while S2=0. And in all cases the measured induced field Bi looks quite reasonable.
This seems quite unexpected. But these results have been measured many times with lab quality instrumentation and different hardware, including different large magnets used to set up the uniform magnetic field. And these results were obtained with several magnetic materials; it need not be a ferrite.