Question

If the horizontal and vertical components of earth’s magnetic field are equal, then angle of dip is:
$\begin{align}
  & \left( A \right){{60}^{\circ }} \\
 & \left( B \right){{45}^{\circ }} \\
 & \left( C \right){{30}^{\circ }} \\
 & \left( D \right){{90}^{\circ }} \\
\end{align}$

Answer 1

Hint: The ratio of the earth’s vertical component of magnetic field to the earth’s horizontal component of magnetic field is called angle of dip. Given in the question that both the horizontal and vertical components of earth’s magnetic field are equal. Thus, the ratio of horizontal and vertical components of earth’s magnetic field is equal to one. Then to calculate the angle of dip, take the inverse tangent of one. That will be the angle of dip.
Formula used:
The tangent for the angle of dip is given by,
$\tan \theta =\dfrac{{{B}_{V}}}{{{B}_{H}}}$
where, $\theta $ is the angle of dip
${{B}_{V}}$ is the vertical component of earth’s magnetic field
and ${{B}_{H}}$ is the horizontal component of earth’s magnetic field.

Complete step by step solution:
The tangent for the angle of dip is given by,
$\tan \theta =\dfrac{{{B}_{V}}}{{{B}_{H}}}$
Thus by substituting the values of ${{B}_{V}}$ the vertical component of earth’s magnetic field and ${{B}_{H}}$ the horizontal component of earth’s magnetic field we get,
Also given in the question is that the ratio of vertical component of earth’s magnetic field is equal to the horizontal component of earth’s magnetic field. Thus their ratio is equal to one.
$\Rightarrow \tan \theta =\dfrac{{{B}_{V}}}{{{B}_{H}}}=1$
Here $\theta $ is the angle of dip. Hence to find $\theta $take the inverse tangent of one.
$\Rightarrow \theta ={{\tan }^{-1}}\left( 1 \right)$
The inverse tangent of one is 45 degrees. Therefore,
$\Rightarrow \theta ={{45}^{\circ }}$

Hence option (B) is correct.

Note:
The tangent for the angle of dip is the ratio of the vertical component of earth’s magnetic field to the horizontal component of earth’s magnetic field. Since, the horizontal and vertical components of earth’s magnetic field are equal, their ratio equals one. Then the angle of dip will be the inverse tangent of one. This is a general equation for finding the angle of dip.