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Torque on soft ferromagnetic objects

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Of more significance is the torque on a soft ferromagnetic object. The torque on an unsaturated object is

(2.17)

Remarkably this is also independent of susceptibility, depending upon the square of B0 (so four times greater at 3 T compared with 1.5 T), with a maximum value within the magnet bore. Torque becomes larger for long needle‐like objects (Figure 2.22b). For a saturated object the torque becomes proportional to Bsat 2 and has a maximum value (Figure 2.23)

(2.18)


Figure 2.23 Predicted torque for ferromagnetic 0.1 kg objects of varying l/d ratios, with density 8000 kg m−3, susceptibility of 1000 and Bsat = 2 T on the axis of a 1.5 T shielded magnet. The bore entrance is at 0.8 m.

Usually an object will twist long before it reaches the bore, and hence the torque rapidly disappears, aligning the object for maximum projectile velocity. There is the possibility of serious injury if an implant is ferromagnetic.

Essentials of MRI Safety

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