Would two Neodymium magnets stick together with twice the power?

Question

Assume I use a coil to create B-flux and put ONE Neodymium cylinder magnet (1" diameter & 0.25" thick) close to the flux, it would create 10 lbs of force. Does that mean that putting TWO cylinder magnets (1" diameter & 0.25" + 0.25" = 0.5" thick) would create 20lbs of force?

Answer 1

Probably not, but it depends on the geometry of your coil.

For a couple of dollars at the hardware store you can get a big stack of those coin magnets. If the answer to your question were yes in general, it'd be harder to break apart the big stack of magnets that to separate two of them. That's not consistent with my experience.

In general for a dipole $\vec m$ in a field $\vec B$, the force is $\vec F=-\nabla(\vec m \cdot \vec B)$. If the dipole moment is a constant, and the dipoles are free to rotate, they will orient themselves so that $\vec m$ is antiparallel to $\vec B$. In that special case, the force simplifies to $$\vec F \approx m \vec\nabla B. $$ In other words, the dipoles "want" to align antiparallel to the field, then to move up the gradient into the strongest part of the field. A dipole in a uniform field feels a torque, but not a net force.

If your coil is set up to generate a uniform field, your two stacked magnets will feel the same force — but that force will be zero. If your coil is generating a magnetic field with some dipole component, your stacked magnets will rotate to align with the field, then (since we've already assumed there is a field strength gradient) one of them will see a weaker gradient than the other. The gradient $\vec\nabla B$ typically vary like $1/r^4$, where $r$ is the distance from the center of the coil, so the force on the two coin magnets can vary considerably over a short distance. This is why strong magnets like to suddenly "leap" together and pinch your fingers when you are playing with them.

Now you could put your two coin magnets next to each other, symmetrically about the axis of your coil, and they would see the same $|\vec\nabla B|$ in slightly different directions. But with the two coin magnets next to each other, they would exert torques on each other, since they prefer to be stacked pole-to-pole; you could engineer a solution like this, but there would be extra parts involved.

I actually happened to have some magnets with this shape on my desk. In response to Carl's comment, I built a little string lifting harness to measure the force on a single magnetized paper clip:

Adding a second magnet increased, but didn't double, the weight that the harness could hold:

stacked number of clips magnets that stayed up 1 11 2 17 3 23 4 24 5 24

The dominant effect in calculating the force is the field is right at the surface of the stack of magnets; it looks like that gets saturated, an effect I didn't consider in the first part of my answer.