# Force on solenoid in external uniform field?

1. Feb 1, 2012

### neosocra

A solenoid, of sufficient length to consider external flux to be zero, passes through a uniform magnetic field with significant length on both ends extending beyond the field.

Will a torque be exerted upon the solenoid ? Or do the windings effectively mask the internal solenoid field from the external? (again, with each solenoid pole well beyond the field; a very long permanent magnet would receive a torque, I'd imagine)

Would the vector orientation of the external uniform field relative to the B vector of the solenoid make any difference?

2. Feb 1, 2012

### clem

There would be the same torque as on a permanent magnet proportional
kXB (k is a vector along the axis of the solenoid.).

3. Feb 1, 2012

### neosocra

Since the external field of the solenoid is in opposite direction than the internal concentrated flux, I could see that field interfacing with the uniform external field, but with an opposite B vector. Is that what you mean?

4. Feb 1, 2012

### clem

The external uniform magnetic field acts ONLY on the current in the solenoid.
The result, though, is the same as if the solenoid were replaced by a permanent magnet.
Magnetic fields don't create force on other fields.

5. Feb 1, 2012

### Philip Wood

Each turn in the solenoid is almost a plane coil in itself, and experiences a pure couple in an external field. The couples on all the turns add together. The fact that the turns are staggered apart in space makes no difference to the addition.

There is, in fact a small BILsin(theta) force on the solenoid because there is a flow of current parallel to the solenoid axis, owing to the helical nature of the solenoid. [When Ampere was doing his pioneering experiments in the 1820s, and trying to make a pivoted solenoid behave like a magnet, he was at pains to neutralise this parallel-to-axis current with one in a wire running the other way.]

6. Feb 1, 2012

### neosocra

I simultaneously agree, and say "wait but..." to myself. Think about the classic method of visualizing the orbital magnetic field from a straight conductor and how that field creates flux density changes as the FIELDS intersect (or more accurately, Don't intersect) causing attraction on the point in the orbit parallel to the uniform field and repulsion when opposite (same analogy as parallel wires of same or opposite direction) *image attached*

I'm well aware that this is done as a tool to visualize effect and not the true cause of force that does come down to point charges in the conductor moving in the current. However, think of the Gilbert model for closely estimating forces between two magnets as point charges on the pole faces. Now we've modeled electrical charges in conductor as magnetic field / magnetic field interaction, and yet magnets as pretend electrical charges. However, in permanent magnet there is no moving point charge, only magnetic fields...

So it'd seem that the fact that no flux is measured outside a (long) solenoid then the effect from that current, add more specifically the charges its comprised of, is redirected by influence of neighboring loops, and thus my hypothesis of the uniform external field passing through a section would likewise not interact with those flowing charges, no matter how you model it... I'm also, like I lead off, expecting I'm wrong, I'm just not Yet reading an invalidation of my false (?) assumptions

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Last edited: Feb 1, 2012