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Question 5.13: Find the magnetic dipole moment of the “bookend-shaped” loop...

Find the magnetic dipole moment of the “bookend-shaped” loop shown in Fig. 5.52. All sides have length w, and it carries a current I .

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This wire could be considered the superposition of two plane square loops (Fig. 5.53). The “extra” sides (AB) cancel when the two are put together, since the currents flow in opposite directions. The net magnetic dipole moment is

\pmb{m}=I\omega ^{2}\hat{\pmb{y}}+I\omega ^{2}\hat{\pmb{z}};

 

its magnitude is   \sqrt{2}I\omega ^{2}, and it points along the 45° line z = y.

5.53

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