Qualitative explanation of Magnetic Braking

[phantomvommand]

When a magnet moves near a non-magnetic conductor such as copper and aluminium, it experiences a dissipative force called magnetic braking force. I am rather confused by the following explanation of magnetic braking force:

The non-magnetic conductor here is the aluminium 'wall' seen on the slope, and the magnet is the doughnut-shaped ring seen rolling down.
Firstly, do let me know if the following explanation for why the current is circular is correct: Because the flux through a portion of the wall is increasing as the magnet moves nearer to it, the current induced produces a B-field to repel the incoming magnet, so as to reduce magnetic flux.

Given that the current is circular, and anticlockwise, I understand why there is the force $F_{M-C}$ acting on it. However, how does the reaction force come about?

 

[Charles Link]

I don't know that the above is the best description of the direction of the forces. The creation of electrical currents by Faraday's law will cause a loss of energy from the source that created them. The direction of the currents is determined by Lenz's law,(the current will travel in a loop=assigning a direction of linear momentum to this loop is IMO incorrect, until magnetic dipole repulsion is included.) Regardless of which direction the magnet is moving, the effect of its interaction with the conductor will be to slow it, and electrical currents will be generated that cause heating of the conductor.

Note: There is a magnetic dipole repulsion that occurs here, (with the current loops in the conductor being the other dipoles), but I think the loss of energy from the ohmic heating may also be important in computing how much the magnet is slowed. (The better the conductor, the stronger the currents=stronger magnetic dipoles with more dipole repulsion, and more ohmic heating= the two effects are hard to separate).

Note 2: A magnetic dipole is any current loop. If the current in the loop is counterclockwise, the north pole is on top, and the south pole on the bottom. Like (di)poles when facing each other are repelled.

Note 3: Meanwhile any magnet with a north and south pole can also be considered to have surface currents circulating in a counterclockwise direction when the north pole is on top.

 

[phantomvommand]

I don't know that the above is the best description of the direction of the forces. The creation of electrical currents by Faraday's law will cause a loss of energy from the source that created them. The direction of the currents is determined by Lenz's law,(the current will travel in a loop=assigning a direction of linear momentum to this loop is IMO incorrect, until magnetic dipole repulsion is included.) Regardless of which direction the magnet is moving, the effect of its interaction with the conductor will be to slow it, and electrical currents will be generated that cause heating of the conductor.

Note: There is a magnetic dipole repulsion that occurs here, (with the current loops in the conductor being the other dipoles), but I think the loss of energy from the ohmic heating may also be important in computing how much the magnet is slowed. (The better the conductor, the stronger the currents=stronger magnetic dipoles with more dipole repulsion, and more ohmic heating= the two effects are hard to separate).

Note 2: A magnetic dipole is any current loop. If the current in the loop is counterclockwise, the north pole is on top, and the south pole on the bottom. Like (di)poles when facing each other are repelled.

Note 3: Meanwhile any magnet with a north and south pole can also be considered to have surface currents circulating in a counterclockwise direction when the north pole is on top.

This is an interesting take on the phenomenon. I gather that your explanation is that kinetic energy is converted to heat energy, thus slowing down the magnet. I understand this explanation, but may I know how the forces argument works? I am still confused about the “reaction force” due to Newton’s third law.

I am thinking that 2 currents are actually induced. In the portion of the wall which the magnet is rolling towards, the magnetic field should be opposite to the field of the magnet (repulsive), and in the portion of the wall which the magnet is rolling away from, the field induced should be attractive. Is this the reason why it slows down, because the front is being repelled and the back is being attracted?

I realize that the diagram only included 1 wall; there should actually be another aluminium wall on the other side of the magnet, although this should not change anything

 

[Charles Link]

Faraday's law says EMF's get generated, and the associated electric fields will put electrons in motion. These charges will also experience magnetic fields. The force on the moving magnet appears to be mostly of the magnetic dipole kind. Perhaps someone else can offer a simpler explanation, but other than considering it as a dipole repulsion that occurs, the complete analysis of what happens in the aluminum is rather complex.

 

[phantomvommand]

Faraday's law says EMF's get generated, and the associated electric fields will put electrons in motion. These charges will also experience magnetic fields. The force on the moving magnet appears to be mostly of the magnetic dipole kind. Perhaps someone else can offer a simpler explanation, but other than considering it as a dipole repulsion that occurs, the complete analysis of what happens in the aluminum is rather complex.

Would I be correct to say that 2 “dipoles” are generated, 1 dipole that repels the front of the doughnut magnet, and another dipole that attracts the back of the magnet?
Something like eddy current brakes, but in this case the magnet is moving.

 

[Charles Link]

See Note 2 of post 2 above. You can consider the current loops in the aluminum to be magnets with a north pole and a south pole. If the north pole of the moving magnet is closer to the aluminum, and moving toward it, the north poles of the current loops in the aluminum will be facing the magnet, with the south poles farther away, and thereby repulsion occurs.

 

[phantomvommand]

See Note 2 of post 2 above. You can consider the current loops in the aluminum to be magnets with a north pole and a south pole. If the north pole of the moving magnetic is closer to the aluminum, and moving toward it, the north poles of the current loops in the aluminum will be facing the magnet, with the south poles farther away, and thereby repulsion occurs.

Thanks for the help!