Where Will a Current Loop Tend to Go When Placed in Different Positions?

[Chimico]

I was reasoning about this matter and i found myself asking a question ... i tried to search the answer in quite a number of books (mainly Physics_For_Scientists_And_Engineers_6_Ed._By_Serway_And_Jewett and and Physics_by_James_S_Walker) but no way ... all the information i found are related to simple expamples (which are always the same) but i am thinking about a different thing ... hope someone can help me with this. I will try to articulate my thought in 3 main points:

1) What i have undestood is that a magnetic field B can exert on a current loop a torque because of the Lorentz force (to say it simple). The standard equations that i found in the Serway book are clear about this. So, for example, there is a rectangular (the shape, however, doesn't really matter) current loop that lies on the z-y plane. The magnetic field B is a vector in the -x direction. The magnetic moment μ of the current loop is the green vector. The green vector and the B vector form a theta θ angle of 45 degrees (position 2). The red dot represents the turning axis. So, now because of the torque exterted on it, the current loop will tend to reach position 1, where the green vector is parallel to the B vector. For position 1 the torque tau is zero. To summerize the behavior of the loop i would say that if i put the loop in position 2, it will tend to naturally assume position 1.

Here is an image of this first example:

[PLAIN]http://www.box.com/s/795zgprlp5tzumpb8lhg

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2) The above one is the classical example. It is possible to make it a little more complicated by considering this situation:

[PLAIN]http://www.box.com/s/5echv3brqbnnusz904n4

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If i put the loop in position 3, it will then go torough position 2 and finally reach position 1.

3) Now, this is the things i didn't find, what happens if i put the loop in a new position (position 4) that has a theta angle > 90 degrees like, for example, this:

[PLAIN]http://www.box.com/s/6udeqaku49quey71mmnb

[/PLAIN]

Will the loop still tend to reach position 1 where the μ magnetic moment is in the same direction as vector B? Since in position 1 the torque is zero i guess it is a stable position so it seems logical to state that the loop will go from position 4 to position 1.

But ... i asked myself ... is there any other position where there is no torque? is there any other postion where to loop will likely go? Well, i noticed that also position 5 has a zero torque:

[PLAIN]http://www.box.com/s/umo06538am6u5m53fi70

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So, in conclusion, if i place the current loop in position4, where will it go? To position1 or position 5? And why?

Thanks in advance to anyone that would like to discuss the matter :-)

 

[gtoguy97]

To answer your question, the current loop will tend to reach position 1 in both cases. This is because the torque on the loop is proportional to the angle between the magnetic moment and the magnetic field, and the torque is the greatest when they are perpendicular (as in position 4). Thus, the loop will try to align itself so that the angle between the magnetic moment and the magnetic field is minimized, which is when they are parallel (position 1). Position 5 has a zero torque, but since it is further from position 4 than position 1, the loop will not likely go to position 5.