Question

The earth's magnetic field at a certain place has a horizontal component $0.3$ gauss and the total strength $0.5$ gauss. The angle of dip is

• A. $\tan ^{-1} \frac{3}{4}$
• B. $\sin ^{-1} \frac{3}{4}$
• C. $\tan ^{-1} \frac{4}{3}$
• D. $\sin ^{-1} \frac{3}{5}$

Answer 1

Answer: (C)

$B^{2}=B_{V}^{2}+B_{H}^{2}$
$\Rightarrow B_{V}=\sqrt{B^{2}-B_{H}^{2}}=\sqrt{(0.5)^{2}-(0.3)^{2}}$
$=0.4$
Now, $\tan \phi=\frac{B_{V}}{B_{H}}=\frac{0.4}{0.3}=\frac{4}{3}$
$\Rightarrow \phi=\tan ^{-1}\left(\frac{4}{3}\right)$