Question

The vertical component of earth’s magnetic field at a place is $\sqrt 3 $ times the horizontal component, the value of angle of dip at this place is?
A) ${30^\circ }$
B) ${45^\circ }$
C) ${60^\circ }$
D) ${90^\circ }$

Answer 1

Hint: In order to find the correct option of the given question, first of all we need to know the relation between angle of dip and the components of the magnetic field. Using the relation and solving it, we can easily conclude the required angle of dip.

Complete step by step solution:
We already know that, Magnetic field is a vector quantity and is represented by $'\vec B'$.
Since, the magnetic field is a vector quantity; it will have its horizontal and vertical components.
The horizontal component is represented as $'{B_{_H}}'$ and the vertical component is represented as $'{B_V}'$.
We can find the angle of dip, by using the relation below,
$\tan \theta = \dfrac{{{B_V}}}{{{B_H}}}$……………… (i)
Now, from the question we can write the ratio of vertical component to the horizontal component as $\dfrac{{{B_V}}}{{{B_H}}} = \dfrac{{\sqrt 3 }}{1}$
Using the above ratio in equation (i), we get,
$\tan \theta = \dfrac{{\sqrt 3 }}{1}$
$ \Rightarrow \theta = {\tan ^{ - 1}}\left( {\dfrac{{\sqrt 3 }}{1}} \right)$
$\therefore \theta = 60^\circ $
Therefore, the required angle of dip is $60^\circ $

Hence, option (C), i.e. $60^\circ $ is the correct choice for the given question.

Note: We should know this fact the angle of dip is the angle between the direction of earth’s magnetic field and the horizontal line of the magnetic meridian. In some of the textbooks you will find that the angle of dip is mentioned as magnetic dip. One can find different values of angle of dip at different points as the magnetic field lines of earth keep changing due to the motion of the earth. For example, at the equator, the angle of dip will be ${0^\circ }$ as at the equator the magnetic field lines are totally horizontal.