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The relation amongst the three elements of Earth's magnetic field, namely horizontal component HH, vertical component VV and dip angle δ\delta is: (BEB_E = total magnetic field):

A

V=BEtan⁡δ,H=BEV=B_E \tan \delta, H=B_E

B

V=BEsin⁡δ,H=BEcos⁡δV=B_E \sin \delta, H=B_E \cos \delta

C

V=BEcos⁡δ,H=BEsin⁡δV=B_E \cos \delta, H=B_E \sin \delta

D

V=BE,H=BEtan⁡δV=B_E, H=B_E \tan \delta

Step-by-Step Solution

  1. Definitions: The total magnetic field of the Earth (BEB_E) at any point on its surface acts at an angle to the horizontal. This angle is called the angle of dip or magnetic inclination (δ\delta).
  2. Vector Resolution: The magnetic field vector BEB_E can be resolved into two rectangular components:
  • The Horizontal Component (HH): This component lies along the horizontal direction. Since δ\delta is the angle with the horizontal, HH is the cosine component. H=BEcos⁡δH = B_E \cos \delta
  • The Vertical Component (VV): This component lies along the vertical direction. It is the sine component. V=BEsin⁡δV = B_E \sin \delta
  1. Conclusion: The correct relationship representing the components is V=BEsin⁡δV=B_E \sin \delta and H=BEcos⁡δH=B_E \cos \delta.
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