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I'm taking an electromagnetism physics course right now, and we did a lab involving a series of U-shaped magnets aligned like a tunnel and a current running through them. We measured the apparent weight of the magnets to demonstrate that the current moving through the magnetic field produces a force on the magnets.

Now, I then started playing around with rearranging the magnets. In the lab, they were all arranged as such (top down view): $$ \begin{align} &NNNNNN\\ &S\hspace{0.5mm}S\hspace{0.5mm}S\hspace{1mm}S\hspace{0.5mm}S\hspace{0.5mm}S \end{align} $$

I rearranged them as such:

$$ \begin{align} &NNNS\hspace{0.5mm}S\hspace{0.5mm}S\\ &S\hspace{0.5mm}S\hspace{0.5mm}SNNN \end{align} $$

Assume the current is flowing from left to right in those diagrams. I was thinking about what the magnetic field would be and how the force on the magnet would be applied. With the first arrangement, the magnetic field flows north to south the whole way and by simple right hand rule, the electrons are coming out of the page (since v x B is into the page, and electrons are negative). The equal and opposite force then pushes the magnets into the page, or downward, increasing the apparent mass. (Correct me if I have that backwards)

With the second arrangement, I figured that by the same principle, the left side of the magnet would be pushed down while the right half of the magnet was lifted down, creating a torque about the center of mass. To test this, I placed the magnets balanced with each end on a different scale. I then induced a 4 Amp current, and... nothing. No change in apparent mass.

I tried calculating what should be happening to no avail. The magnet rig weighed 158 grams normally, and the scales could only read to 1 gram changes. Was I correct in my prediction, but the scales couldn't read the change as it was too small? Or is something else happening with the forces on the magnets?

EDIT: There are 6 separate N/S magnets, all connected to each other along a base plate but removable. When I rearranged them, I took the three on the right and flipped them around. I expected opposite forces, but in different places, creating a torque. I'll try to illustrate a front view below, with O/X being the magnetic field of the N/S magnet in that position (out of and into the screen respectively):

$$ \begin{align} &↓\hspace{1mm}↓\hspace{1mm}↓\hspace{1mm}↑\hspace{1mm}↑\hspace{1mm}↑\\ &O O O X X X\\ \end{align} $$

The arrows there are the forces I expected to be occuring on each segment of the rig. This would then produce a torque counterclockwise about the center, in between the sets of 3 magnets.

Also, if anyone knows how to better format or illustrate this, let me know.

EDIT 2: I'll explain he results here better. After arranging the magnets, I induced the 4 Amp current through the center of the "tunnel" of magnets. The actual results were - nothing. There was no change in apparent mass on either side with any amount of current up to 10 Amps. Meanwhile, I expected one of the scales to show an increase in apparent weight, with the other scale showing an equal decrease in apparent weight. This did not happen.

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  • $\begingroup$ Did you measure a difference in the weight of the magnets when you switched the current on/off? What was this difference? ... The direction of conventional current is the direction in which +ve charge flows, not the direction in which -ve electrons flow. $\endgroup$ – sammy gerbil Mar 28 '18 at 17:53
  • $\begingroup$ @sammygerbil The difference in weights with the current off was 0; they were positioned so that each balance had 74g of the weight. Then we turned the current on, and the weight did not change. In the first arrangement, on the other hand, turning the 4A current on induced a change of 2g on the whole magnet. $\endgroup$ – Vedvart1 Mar 28 '18 at 18:04
  • $\begingroup$ I don't understand where the 74g comes from since 2 x 74g = 148g not 158g. ... So in the 1st arrangement the wire pulls up (or pushes down?) with 1g force on each set of 3 magnets? Then if you reverse one set of magnets the wire should push down with 1g force on one side and pull up with 1g force on the other side, a total force of zero, making no change to the weight of the rig. Isn't that the result you expected, and the result that you got? $\endgroup$ – sammy gerbil Mar 28 '18 at 18:19
  • $\begingroup$ Sorry, I didn't have the numbers on me and did the math in my head since I just remembered they added up. It was 79g. I clarified the setup in the question edit. $\endgroup$ – Vedvart1 Mar 29 '18 at 0:29
  • $\begingroup$ I think I understood what you did but you are still being very unclear about what result you got. Please could you state exactly what measurements you made and what the results were. $\endgroup$ – sammy gerbil Mar 29 '18 at 5:03
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Your thinking is correct : in arrangement 2 you should expect a torque, causing the weight on one side to increase by 1g and that on the other side to decrease by 1g.

The trouble is that if the smallest increment is 1g then a change from 79g to 80g might in fact be from 79.97g to 80.01g (ie 0.01g for each Amp). I presume that in arrangement 1 also you increased the current up to 10A but still saw no increase in weight above 1g on each side. The weight could in fact have increased to 80.07g, but this would still be registered as 80g.

If the contacts between the scales and the magnet rig were single points, then the torque in arrangement 2 ought to have been detected even with the above limitation. However, if contact is made across flat surfaces, then it is possible for the distribution of weight to shift due to small changes in the orientation of the rig. This happens in Equilibrium of a tower of 2-d blocks and How is weight distributed in a stack of boxes?

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