Sliding Magnet off of Steel
Most recent answer: 09/18/2013
Hi Adam- I combined your two related questions.
The simple sliding part is easy. As you slide the magnet around on the steel plate, the magnetic energy hardly changes. So you're just fighting friction, as you supposed. As you slide the magnet close to the edge of the plate, some of the field lines now spill out, so you're gradually increasing the magnetic energy. That takes a little extra force, beyond the friction, but since it's gradual the force isn't too high. By the time you've gotten the magnet next to the table edge, its binding energy to the steel is reduced significantly, although not quite by a factor of 2, I think. That would make it easier to pull away from the steel than if it were in the middle.
I think, from having done this many times, that there's an additional effect- it's just easier bio-mechanically to grab the the magnet and push it part-way off and then to pull it the rest of the way once it's mostly off. If you try to just pull it off from the middle of the table, you not only have more binding energy to overcome but also you can only apply force by the friction of your fingers on the magnet sides. That's harder to do than simply pushing it via a normal force.
(published on 09/18/2013)
Follow-Up #1: energy and force
Adam- I've combined your two new questions.
Aha, I should have spelled out the force-energy connection. If the energy changes by and amount dE as the magnet is moved a distance dx, the force required is dE/dx. So the force required can be reduced either by reducing the energy change or by spreading it out over a bigger distance.
I think that when the magnet is almost at the edge, the energy has already been gradually increased a little less than halfway toward the value that it would have when it's fully removed. It's not real clear to me, although somebody probably has solved just this problem, exactly how different the pattern is for the energy increase as you slide it off the rest of the way, compared to the pattern if you pulled it straight off.
It is a very familiar fact to anybody who uses things like this that the sliding is easier.
By "normal" force, we mean the force when one thing pushes on another. It's usually much simpler to exert large normal forces than larger frictional forces. Think of a big heavy box on the floor. You may be able to just shove it forward without too much trouble. It'll be much harder to grab the sides and drag it.
So I'm not sure how much of the difference in ease of that last pull is due to it just being easier to apply the force by pushing and how much is due to the required force being lower. There are some experiments you could use to test it. For example you could take a little calibrated force-applier, maybe a string that stretches as a function of tension, and compare things more precisely.
(published on 09/20/2013)
Follow-Up #2: forces between magnet and steel
What I meant there is that for any particular position of the magnet with respect to the steel plate, the net magnetic field pattern in space can be caclulated. The calculation is a bit tricky, especially if the steel is magnetizing past the range where the magnetization is linear in the applied field. The complicated geometry near the edge also makes the calculation tricky. Nevertheless, there are computer codes for doing these calculations numerically. The energy can be calculated from an integral over space of the local energy density stored in the magnetic field. The force is then just given by how that net energy changes with position.
Here's a quick search result for some field calcualtion programs:
(but this one, complicated enough as is, doesn'tseem to include the permeable material)
This one should give you the bare field from the magnet without the steel: .
This one seems to work with steel but only for cylinders: .
You may have to pay to get a fully usable program that can handle both the messy geomery and the non-linear steel.
Although the maximum force is likely to be much less for sliding, and easier to apply, the net integral of force times displacement will be a bit larger for sliding, because in addition to the work needed to increase the magnetic energy you also have the work done against friction.
(published on 09/23/2013)