The relation amongst the three elements of Earth's magnetic field, namely horizontal component $H$, vertical c

Question

The relation amongst the three elements of Earth's magnetic field, namely horizontal component $H$, vertical component $V$ and dip angle $\delta$ is: ($B_E$ = total magnetic field):

Accepted Answer

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

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