Relation between I,H,V and δ
Let I be the total intensity of Earth’s field and δ be the angle of dip.
In fig, AI represents the total intensity of the earth’s magnetic field ∠BAI = δ. The resultant I is resolved into two rectangular components :
Horizontal component along OB is
H = I cosδ ………(1)
Vertical component along OV is
V = I sinδ ……….(2)
Dividing equ. (2) by equ. (1), we have
V/H = I cosδ / I sinδ
V/H = tanδ ……..(3)
Also by squaring and adding Equ. (1) and (2),
Case I. At the magnetic equator, i.e., δ = 0
Hence, by equ. (3) , tan 0 = V/H
0 = V/H
V = 0
and by equ. (4), putting V = 0 then I = H
Hence, at magnetic equator the vertical component is zero and total intensity of earth’s field is equal to the horizontal component.
Case II. At magnetic poles. i.e. δ = 90
tan90 = V/H
∞ = V/H
Thus, at the poles only vertical components acts.
Now, by equ. (4)
I = V
Thus, at poles the total intensity is equal to the vertical component.
Case III. If δ = 45, then
tan45 = V/H
1 = V/H
V = H
Hence, the place where V = H, then angle of dip will be equal to 45.