The idea that a magnetic field can have therapeutic value has beenaround for cen

Question

The idea that a magnetic field can have therapeutic value has beenaround for centuries. A rare-earth magnet sold to relieve jointpain is a disk 1.20 mm thick and 3.50 mm in diameter. Its circularflat faces are its north and south poles. Assume it is accuratelymodeled as a magnetic dipole. Also assume B ˜(0) /(2x3) describes the magnetic field itproduces at all points along its axis. The field is strongest, withthe value 32.1 mT, at the center of eachflat face. At what distance from the surface is the magnitude ofthe magnetic field like that of the Earth, with a value of45.2 µT?
1 mm

Explanation / Answer

The field at points on the axis of the diskvaries as                              B ˜ (0) /(2x3)                                 ˜ k / x3 Where k is constant            xis the distance from the midplane of thedisk


At the surface of the disk we have           x1 = thickness / 2              = 1.20 mm / 2              = 0.60 mm            B= 32.1 mT So that the constant k =Bx13                                   = 32.1 x 10-3 T * (0.60mm)3 At the distance from the center of the disk toheight where B = 45.2 x 10-6 T is                      x2  = (k / B)1/3              = (32.1 x 10-3 T * (0.60mm)3 / 45.2 x10-6 T)1/3               =5.35 mm At the distance from the center of the disk toheight where B = 45.2 x 10-6 T is                      x2  = (k / B)1/3              = (32.1 x 10-3 T * (0.60mm)3 / 45.2 x10-6 T)1/3               =5.35 mm The distance from the surface is the magnitudeof the magnetic field like that of the Earth, with a value of 45.2µT  is           x = x2 - x1              = 5.35 mm - 0.60 mm              = 4.75 mm              = 5.35 mm - 0.60 mm              = 4.75 mm                  

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