a 39 p p 39 n n 39 e e 39 where the material is sufficiently anisotropic that the field crosses only the boundaries of the surface a a 39 p p 39 and the surface e e n n 39 this yields where subscript 34 a 34 refers at section nn 39 pp 39 to the air gap and subscript 34 m 34 refers to the magnet material because da m da a cos u03b8 equation 4 becomes most rare earth magnets have b r u2243 h c and if g d is small typically less than 0 3 equation 9 simplifies to referring to fig4 if magnet 26 rotates by an angle u03b3 relative to coils 32 and 34 the field b u at segment u03bc of coil 32 is derived from equation 1 where u03b8 45 u00b0 u03b3 the resulting torque t on coil 32 having n turns of wire from a current i is derived from lorenz forces noting that forces at segments u and v are in opposition because the current flows in opposite directions in the two halves of coil 32 we find that t 0 707 k b sub r l n i d sin u03b3 13 where l is the length of the segment and d is twice the radius where the coil segment is located and approximately the diameter of the magnet for small angles equation 13 yields approximately as coil 32 is attached to the shell 30 t is also the torque acting upon the frame of scanner 10 which is normally held fixed.