Question

If a dip circle is placed in a vertical plane at an angle of 30° to the magnetic meridian, the dip needle makes an angle of 45° with the horizontal. The real dip at that place is
\[\begin{align}
  & \text{A}\text{. ta}{{\text{n}}^{-1}}\left( \dfrac{\sqrt{3}}{2} \right) \\
 & \text{B}\text{. ta}{{\text{n}}^{-1}}\left( \sqrt{3} \right) \\
 & \text{C}\text{. ta}{{\text{n}}^{-1}}\left( \dfrac{\sqrt{3}}{\sqrt{2}} \right) \\
 & \text{D}\text{. ta}{{\text{n}}^{-1}}\left( \dfrac{2}{\sqrt{3}} \right) \\
\end{align}\]

Answer 1

Hint: To find the angle of dip we have to find out the vertical component and horizontal component of earth’s magnetic field in the magnetic meridian.

Formula used: Angle of dip = \[\tan \theta =\dfrac{v}{h}\]

Complete step by step solution:
Let us assume the vertical component and horizontal component of earth’s magnetic field at magnetic meridian as v and h respectively.
Angle of dip which is defined as the angle made by the earth’s magnetic field line with the horizontal is given by,
 \[\tan \theta =\dfrac{v}{h}\]……………. (i) [where, is the dip angle]
We should consider the angle of dip to be positive when the magnetic field lines point downwards and negative when the magnetic field lines point upwards.
For 30° to the meridian and 40° to the horizontal,
\[\begin{align}
  & \tan \theta =\cos {{30}^{\circ }} \\
 & \Rightarrow \theta ={{\tan }^{-1}}\dfrac{\sqrt{3}}{2}..........(ii) \\
\end{align}\]
Comparing equation (i) and (ii) we get,

Therefore, the answer is \[{{\tan }^{-1}}\dfrac{\sqrt{3}}{2}\] which is option A.

Additional information: The angle of dip varies from point to point which provides the information related to the motion of the earth’s magnetic field. The angle of dip is 0° when the dip needle rests horizontally and the angle of dip is 90° when the dip needle rests vertically. When the horizontal component and the vertical component of earth’s magnetic field are the same, the angle of dip is equal to 45°.

Note: The angle of dip plays an important role in geographical field mapping. In the development of any geological map, the angle of dip is examined without a degree sign. For any tilted bed, the dip helps in providing the steepest angle of descent as compared to a horizontal plane.