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 ______.

पर्याय

• ${\displaystyle {\tan }^{-1} \frac{3}{4}}$

• ${\displaystyle {\sin }^{-1} \frac{3}{4}}$

• ${\displaystyle {\tan }^{-1} \frac{4}{3}}$

• ${\displaystyle {\sin }^{-1} \frac{3}{5}}$

Answer 1

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 ${\displaystyle \underline{{\tan }^{-1} \frac{4}{3}}}$.

Explanation:

${\displaystyle {\text{B}}_{\text{v}}=\sqrt{{\text{B}}^2-{\text{B}}^2\_\text{H}}=\sqrt{{\left(0.5\right)}^2-{\left(0.3\right)}^2}}$

${\displaystyle {\text{B}}_{\text{v}}=0.4}$

Now, ${\displaystyle \tan \varphi =\frac{{\text{B}}_{\text{v}}}{{\text{B}}_{\text{H}}}=\frac{0.4}{0.3}=\frac{4}{3}}$

${\displaystyle \varphi ={\tan }^{-1}\left(\frac{4}{3}\right)}$