Considering the earth as a short magnet with its centre coinciding with the centre of earth, show that the angle of dip`phi`is related to magnetic latitude `lambda` by the relation `tan phi = 2 tan lambda`.

Explanation

consider the situation as shown in the figure . For dipole , at position ` (r , theta )` we have
`B_r = (mu_0)/(4pi)(2 M cos theta )/(r^(3)) and B_0 = (mu_0)/( 4pi)(M sin theta )/(r^(3))` .......... (1)
and as ` tan phi = (B_V)/(B_H) = -(B_r)/(B_(theta))`, so in the light of eq (1) ,
` tan phi = -2 cot theta `
But from figure ` theta = 90 + lambda `
so , ` tan phi = -2 cot (90 + lambda )` , i.e., ` than phi = 2 tan lambda`.