# Forces between a Solenoid and an External Permanent Magnet

What happens if I have a permanent magnet outside an ideal solenoid? Does the permanent magnet rotate until the system reaches an energy minimum in its magnetic fields? Or does the permanent magnet fail to rotate because the magnetic field of the solenoid does not reach the magnet? Wouldn't there be a magnetic force on the solenoid due to the permanent magnet even though the magnetic field of the solenoid does not reach the permanent magnet?

The more general question is this, "Does non-uniformity of magnetic fields external to a permanent magnet affect the force on the permanent magnet?"

Sincerely,

Kevin M.

CWatters
Homework Helper
Gold Member
What happens if I have a permanent magnet outside an ideal solenoid? Does the permanent magnet rotate until the system reaches an energy minimum in its magnetic fields?

The set up isn't at all clear but if it has infinite rotational symmetry (like a tube in a tube) then why would any one position have a lower energy?

The more general question is this, "Does non-uniformity of magnetic fields external to a permanent magnet affect the force on the permanent magnet?"

Again it's not clear what you are asking.

Take a look at how a permanent magnet brushless DC motor works? The magnets are on the rotor. The windings are on the outside. The windings create a "non-uniform magnetic field external to the permanent magnet on the rotor". The force causes the magnets on the rotor to spin.

The set up isn't at all clear but if it has infinite rotational symmetry (like a tube in a tube) then why would any one position have a lower energy?

Again it's not clear what you are asking.

Take a look at how a permanent magnet brushless DC motor works? The magnets are on the rotor. The windings are on the outside. The windings create a "non-uniform magnetic field external to the permanent magnet on the rotor". The force causes the magnets on the rotor to spin.

In the case of an ideal solenoid, the current in the solenoid does not generate a magnetic field outside of it. If I place a rectangular bar magnet at an arbitrary position outside the solenoid, it does not pick up any magnetic field. Or does it? If there exists a magnetic field inside the solenoid, does the magnetic flux of the bar magnet "attempt" to line up with the lines of flux inside the solenoid, such that the lines of flux attain the path of least reluctance?

In other words, "Does reluctance torque occur between an ideal solenoid and a magnet outside the ideal solenoid?"

Staff Emeritus
In the case of an ideal solenoid, the current in the solenoid does not generate a magnetic field outside of it. If I place a rectangular bar magnet at an arbitrary position outside the solenoid, it does not pick up any magnetic field. Or does it?

You just said it didn't - by definition. If your solenoid has properties different than what you defined them to be, you're not going to be able to get a consistent answer.

You just said it didn't - by definition.

So is that a "no" to the question, "Does reluctance torque occur between an ideal solenoid and a magnet outside the ideal solenoid?"

Staff Emeritus

When I spoke of the case where the rectangular bar magnet may "pick up any magnetic field", what I meant in that scenario is that the presence of a magnetic field can be detected by the object.

I do not mean to imply that the detected field physically overlaps the bar magnet's volume. If I did mean that, of course the answer would be, tautologically, no.

By the phrase "pick up any magnetic field" in this context, I mean that the magnetic field of the solenoid can affect bar magnet. The thought was that the magnetic reluctance would be a function of the bar magnet's orientation and position relative to the solenoid, so I was thinking that there should be forces on the magnet related to the phenomenon of magnetic reluctance.

A field physically remote from the bar magnet, in this case the field inside a solenoid, would be added to the field contributed by the bar magnet, resulting in interaction densities (i.e. force, torque, and energy densities) within the solenoid, which I thought couples to the bar magnet in some way.

Of course, now just realizing that this would defy the concept of locality as it applies to the definition of the field, I am now thinking that these interaction densities are only relevant as far as forces, torques, and field energies that may be impressed upon the solenoid, and not the bar magnet.