Assume the dipole model for earth's magnetic field B which is given by $B_v$ =Vertical component of magnetic field $=\large\frac{\mu_0}{4 \pi}.\frac{2m \cos \theta}{r}$ $B_H$= Horizontal component of magnetic field $\qquad= \large\frac{\mu_o}{4 \pi} \frac{\sin \theta m}{r^3}$ $\theta= 90^{\circ}$- latitude as measured from magnetic equator . Find loci of points for which dip angle is $\pm 45^{\circ}$

Question

$\begin{array}{1 1} \theta = 0^{\circ} \\ \theta= \large\frac{\pi}{2} \\ \theta =\large\frac{\pi}{4} \\ \theta = \tan ^{-1}(2) \end{array}$