- #1
center o bass
- 560
- 2
When one finds the torque on a rectangular current loop one finds that it's equal to
[tex]\vec m \times \vec B[/tex]
where m is the magnetic moment of the loop. I want to generalize this to arbirary current loops with constant current and I found that the torque would be equal to
[tex] \left(I\oint \vec r \times \vec dl\right) \times \vec B[/tex]
so I would think it would be natural to define
[tex] \vec m =I\oint \vec r \times \vec dl [/tex]
for these current loops. However when it up at http://en.wikipedia.org/wiki/Magnetic_moment" I find that the magnetic moment is defined as
[tex]\vec m =\frac{1}{2} I\oint \vec r \times \vec dl. [/tex]
Where does this factor of a half come into the picture? Is'nt 'moments' supposed to be that what generates torques and not just be proportional to it?
[tex]\vec m \times \vec B[/tex]
where m is the magnetic moment of the loop. I want to generalize this to arbirary current loops with constant current and I found that the torque would be equal to
[tex] \left(I\oint \vec r \times \vec dl\right) \times \vec B[/tex]
so I would think it would be natural to define
[tex] \vec m =I\oint \vec r \times \vec dl [/tex]
for these current loops. However when it up at http://en.wikipedia.org/wiki/Magnetic_moment" I find that the magnetic moment is defined as
[tex]\vec m =\frac{1}{2} I\oint \vec r \times \vec dl. [/tex]
Where does this factor of a half come into the picture? Is'nt 'moments' supposed to be that what generates torques and not just be proportional to it?
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