Question

The magnetic dip angle at two places are ${30}^{\circ }$ and ${45}^{\circ }$. The ratio of horizontal components of earths magnetic field at the two places is-

• A. $1:\sqrt{2}$
• B. $\sqrt{3}:\sqrt{2}$
• C. $\sqrt{2}:1$
• D. $\sqrt{3}:1$

Answer 1

The correct option is B $\sqrt{3}:\sqrt{2}$

Horizontal component of earth's magnetic field is

$B_H=B\cos \theta [\because \theta =\text{dip angle}]$

$\Rightarrow {\left(B_H\right)}_1=B\cos {30}^{\circ }$

$\Rightarrow {\left(B_H\right)}_2=B\cos {45}^{\circ }$

$\Rightarrow \frac{{\left(B_H\right)}_1}{{\left(B_H\right)}_2}=\frac{B\cos {30}^{\circ }}{B\cos {45}^{\circ }}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}}=\frac{\sqrt{3}}{\sqrt{2}}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.