# Magnetic attraction and repulsion equivalence

Equations of attraction or repulsion can get very complicated when the field shapes and densities are not identical. Intuition would hold the forces to be the same, but in on closer examination the field shape of two repulsing magnets looks entirely different from two attracting magnets. I specualate the repulsion will be weaker at the same distance than the attraction with all other variables held constant. Comments?

kuruman
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Instead of speculating, perhaps you can consider some equations. The force on a magnetic dipole ##\vec \mu## in an external field ##\vec B## is given by ##\vec F=-\vec \nabla U##, where ##U=-\vec \mu \cdot \vec B.## What happens to the force if you reverse the direction of the external magnetic field all else being equal? Consider the bar magnet as consisting of a collection of dipoles. How can you reverse the direction of the magnetic field generated by the electromagnet keeping everything else the same?

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kuruman
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The link you provided is concerned about calculating the force between two bar magnets. Here we have an electromagnet and a bar magnet. I agree that calculating the force between the two is (at least) as difficult as between two bar magnets, but my point is that you don't need to know what the force looks like to show that, if you change it from attractive to repulsive simply by reversing the current, it changes direction but not magnitude. Note: We assume that there are no hysteresis effects or we can consider two identical setups, one with the current running one way and one with the current running the other way.

Thank you Kuruman, and I take your point. I think my point is I suspect just looking at the shape of the fields involved in attraction versus repulsion that there are two different formulas at work. A simple way to think of it is that many of the lines of force in repulsion go off into space, while all the lines of force connect to the other magnet in attraction.

I am surprised I cannot find any experimental data, I suppose its a problem that doesn't connect to any interesting real world applications.

I think I will run some experiments and find out

kuruman
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A simple way to think of it is that many of the lines of force in repulsion go off into space ...
Don't forget that magnetic field lines always form closed loops. If you draw them on a sheet of paper, the number of lines that cross the perimeter of the paper going out must be equal to the number of lines that cross the perimeter going in. Also don't forget that they do not stop at the south pole and start at the north pole; they just go through the bar magnet.

That is a good point, I take back what I said about the number of lines of force.

Here are a few related questions I am using over
1. Small magnet versus large magnet. Are the NUMBER of lines of force the same , but the larger magnets lines of force are stronger?
2. In attraction it appears some lines of force exist between the poles of the two magnets is that true
3. In repulsion it appears no lines of force connect the two magnets...is that true
4. If 2 and 3 are both true it must be that unequal numbers of lines of force are involved in attraction versus repulsion

kuruman
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1. Size is irrelevant. You can have a magnet half the size of another magnet that can lift twice the weight. If you were to draw lines of force (I prefer the name magnetic flux lines because the magnetic force is not necessarily in the direction of the lines) for the two magnets, the stronger magnet will have more lines per unit area coming out of its north pole.
2 & 3. Not true. Lines exist between the magnets whether they are in attraction or repulsion.
4. I don't see why that follows even if 2 & 3 were true.

You are keen in doing an experiment and I applaud this. Here is a suggestion. I have not tried it, but it might work and does not involve complex or expensive equipment, just the ability to work with your hands.

Get a bunch of small neodymium magnets.
Find a plastic transparent tube whose diameter is slightly larger than the diameter of the magnets.
Glue one magnet on a stand at the bottom of the tube.

Repulsion mode
Drop a second magnet down the tube in repulsion (figure on the left) after you measured its weight.
Record the separation ##y## between magnets.
Add some weight (non-magnetic) and record the new value for ##y##. The force exerted by the bottom magnet on the top magnet is equal to the extra weight plus the weight of the top magnet.
Make a plot of force versus ##y + d## where d is the length of one of the magnets. This will give you the force as a function of the separation between the magnets' midpoints which (I think) is a better description.

Attraction mode
Suspend from a string (how is your call) a magnet and send it down the tube in attraction mode. Tie the other string to an equal arm balance (see figure on the right). Pile enough weight on the pan to hold the magnet to height ##y##. The attractive force exerted by the bottom magnet on the top magnet will be equal to the weight of the pan plus weights minus the weight of the top magnet. Make another plot and compare.

I leave the details to you, but it is important to realize that in attraction mode you don't want the magnets to stick together because then it might be impossible to separate them without taking the whole thing apart. To that effect, I would cut two diametrically opposing vertical slots on the side of the tube and push a non-magnetic but sturdy rod across, (that's the "Stop" in the figure.) It will keep the top magnet from sticking to the bottom magnet and you can also use it to slide the top magnet up without pulling on the string. Also, a thin coating of baby powder inside the tube will keep sticky moisture away and decrease friction.

If you get any results, we will be curious to see them. Good luck.