Relation between I,H, and V

Relation between I,H,V and δ

 

Let I be the total intensity of Earth’s field and δ be the angle of dip.

Relation between I,H, and V

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),

Relation between I,H, and V

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

H=0

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.

 

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