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

& \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{aligned}$$

Answer 1

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,

& \tan \theta =\cos {{30}^{\circ }} \\\ & \Rightarrow \theta ={{\tan }^{-1}}\dfrac{\sqrt{3}}{2}..........(ii) \\\ \end{aligned}$$ Comparing equation (i) and (ii) we get, **Therefore, the answer is $${{\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.