Question

What will be the angle of dip when both the vertical and the horizontal components of the earth's magnetic field are found to be equal?
$\begin{align}
  & A.30{}^\circ \\
 & B.45{}^\circ \\
 & C.60{}^\circ \\
 & D.90{}^\circ \\
\end{align}$

Answer 1

Hint: The dip angle at a certain point is described as the angle between the direction of the magnetic field of the earth abbreviated as $B$ and the horizontal at that point on the surface of the Earth. Therefore the tangent of dip angle is given as the ratio of the horizontal component of earth’s magnetic field to the vertical component of earth’s magnetic field. The values of horizontal and the vertical component of earth’s surface as per mentioned in the question. These all may help you to solve this question.

Complete Answer:
The dip angle $X$ at a point is described as the angle between the direction of the magnetic field of the earth, $B$ and the horizontal at that point on the surface of the Earth.
Therefore, we can write that, the horizontal component of earth’s magnetic field is given as,
${{B}_{H}} =$ horizontal component of earth’s magnetic field
${{B}_{V}} =$ vertical component of earth’s magnetic field
The tangent of the dip angle is given as the ratio of the horizontal component of earth’s magnetic field to the vertical component of earth’s magnetic field.
Therefore we can express this mathematically as,
$X={{\tan }^{-1}}\dfrac{{{B}_{V}}}{{{B}_{H}}}$
Here in the question, it is mentioned as the horizontal component of earth’s magnetic field will be equal to the vertical component of earth’s magnetic field.
That is we can write that,
${{B}_{V}}={{B}_{H}}$
That is the dip angle is given as,
$X={{\tan }^{-1}}\left( \dfrac{{{B}_{V}}}{{{B}_{H}}} \right)={{\tan }^{-1}}\left( 1 \right)=45{}^\circ $
Therefore the dip angle is given as $45{}^\circ $.

Note:
The magnetic declination at that place is given as the angle between the magnetic meridian and geographic meridian at the certain place. Magnetic Inclination is also referred to as the angle of dip. It is defined as the angle between the direction of the total magnetic field of earth and a horizontal line in the magnetic meridian.