If the earth's field induction at a place is 0.36 G and the angle of dip is `30^(@)` , the horizontal and vertical component of the field will be respectively

Options

A. `0.18 G , 0.18 sqrt3 G`
B. `0.18 sqrt3 G , 0.18 G`
C. `0.36 G , 0.36 sqrt3 G`
D. `0.36 sqrt3 G , 0.36 G`

Answer

To solve the problem of finding the horizontal and vertical components of the Earth's magnetic field induction given the total induction and the angle of dip, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Values:**
- Total magnetic field induction, \( B = 0.36 \, \text{G} \)
- Angle of dip, \( \delta = 30^\circ \)

2. **Identify the Formulas:**
- The horizontal component of the magnetic field, \( B_H \), is given by:
\[ B_H = B \cos \delta \]
- The vertical component of the magnetic field, \( B_V \), is given by:
\[ B_V = B \sin \delta \]

3. **Calculate the Horizontal Component:**
- Substitute the values into the formula for the horizontal component:
\[ B_H = 0.36 \cos(30^\circ) \]
- We know that \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \), so:
\[ B_H = 0.36 \times \frac{\sqrt{3}}{2} = 0.18\sqrt{3} \, \text{G} \]

4. **Calculate the Vertical Component:**
- Substitute the values into the formula for the vertical component:
\[ B_V = 0.36 \sin(30^\circ) \]
- We know that \( \sin(30^\circ) = \frac{1}{2} \), so:
\[ B_V = 0.36 \times \frac{1}{2} = 0.18 \, \text{G} \]

5. **Final Results:**
- The horizontal component of the magnetic field is \( B_H = 0.18\sqrt{3} \, \text{G} \)
- The vertical component of the magnetic field is \( B_V = 0.18 \, \text{G} \)

### Summary of the Components:
- Horizontal Component, \( B_H = 0.18\sqrt{3} \, \text{G} \)
- Vertical Component, \( B_V = 0.18 \, \text{G} \)