The exchange coupling as being responsible for ferromagnetism is not the mutual magnetic interaction between two elementary magnetic dipoles. To show this, calculate (a) the magnitude of the magnetic field a distance of 13 nm away, along a dipole axis, from an atom with magnetic dipole moment 1.2 × 10 − 23 J / T, and (b) the minimum energy required to turn a second identical dipole end for end in this field. a) Number ()Unitsb) Number ()Units

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The exchange coupling as being responsible for ferromagnetism is not the mutual magnetic interaction between two elementary magnetic dipoles. To show this, calculate (a) the magnitude of the magnetic field a distance of 13 nm away, along a dipole axis, from an atom with magnetic dipole moment   1.2  ×      10          −      23           J      /    T, and (b) the minimum energy required to turn a second identical dipole end for end in this field. a) Number  ()Unitsb) Number ()Units

avuglantsaew · Accepted Answer

dipole moment   m  =  1.2  ×      10          −      23           J      /    TThe distance   d  =  13  n  m  =  13  ×      10          −      9           mThe magnetic field along the axis is  B  =            μ      0              4      π        ⋅            2      m              d      3          =            4      π      ×              10                  −          7                    ×      1.2      ⋅              10                  −          23                            2      π      ×      (      13      ×              10                  −          9                            )        3              =  1.092  ×      10          −      6           Tb)The energy in magnetic field B to retale a dipole m to angle 0 is  U  =  −  m  B  cos  ⁡  θHere to rotate   θ  =      180          ∘      minimum energy  U  =  −  m  B  cos  ⁡      180          ∘          =  −  1.2  ×      10          −      23        ×  1.092  ×      10          −      6        ×  (  −  1  )    =  1.31  ×      10          −      29           J

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