question_answer 48)

  Assume the dipole model for earth's magnetic field B which is given by  = vertical component of magnetic field;  = Horizontal component of magnetic field ;  = 90° - latitude as measured from magnetic equator. Find loci of points for which (i) is minimum; (ii) dip angle is zero; and (iii) dip angle is ± .

Answer:

                  (i) Given, vertical component of earth's magnetic field, Horizontal component of earth's magnetic field                ...... From , we note that B is minimum if cos  = 0 or which is so, at magnetic equator. Thus, B is minimum at magnetic equator which is the loci of points. (ii) If  is the angle of dip, then tan = . Angle of dip  is zero if  = 0. It will be so if . So, the angle of dip is zero on magnetic equator which is the loci of points. (iii) If  is 45°, then tan 45° = 2 cot  = 2/tan  or tan= 2 or= (2) is the loci of points.