GATE-2018 (24) :Wyllie – Time average equation

5. In the Geomagnetic field, Vertical and Horizontal fields are equal then calculate the magnetic latitude?

Solution:

$\tan i=2 \tan \phi ---(1)$

i= magnetic inclination or dip

φ = magnetic latitude

$\tan i=\frac{V}{H}=\frac{Vertical field}{Horizontal field}$

From given solution,

$V=H$

$\tan i =1 ---(2)$

$i=\arctan(1)=45^{0}$

Substitute eq (2) in eq(1)

$2 \tan \phi=1$

$\tan \phi=\frac{1}{2}$

Magnetic latitude$( \phi )=\arctan (0.5)=26.56^{0}$