• question_answer Obtain relations between (i) earth's magnetic field and its horizontal and vertical components, (ii) angle of dip and the horizontal and vertical components of the earth's magnetic field.

We know that, ${{B}_{H}}={{B}_{E}}\cos \delta$                             ?(i) and       ${{B}_{V}}={{B}_{E}}\sin \delta$                              ?(ii) Here,     ${{B}_{E}}$= Earth?s magnetic field, ${{B}_{H}}$ = horizontal component of magnetic field, ${{B}_{V}}$= vertical component of magnetic field and       $\delta$ = Angle of dip. (i) Squaring Eqs, (i) and (ii) and then adding, we get $B_{H}^{2}+B_{V}^{2}=B_{E}^{2}$ or ${{B}_{E}}=\sqrt{B_{H}^{2}+B_{V}^{2}}$ (ii) Dividing Eq. (ii) by Eq. (i), we get             $\frac{{{B}_{V}}}{{{B}_{H}}}=\tan \delta$ or ${{B}_{V}}={{B}_{H}}.\tan \delta$