The value of horizontal component of earth's magnetic field at a place is `-.35xx10^(-4)T`. If the angle of dip is `60^(@)`, the value of vertical component of earth's magnetic field is about:

Options

A. `0.1 xx 10^(-4)T`
B. `0.2xx 10 ^(-4)T`
C. `0.4 xx 10 ^(-4)T`
D. `0.61 xx 10 ^(-4)T`

Answer

To find the vertical component of the Earth's magnetic field (Bv) given the horizontal component (Bh) and the angle of dip (δ), we can use the relationship between these quantities.

### Step-by-Step Solution:

1. **Identify the given values:**
- Horizontal component of Earth's magnetic field, \( B_H = -0.35 \times 10^{-4} \, T \) (we will use the magnitude, so \( B_H = 0.35 \times 10^{-4} \, T \))
- Angle of dip, \( \delta = 60^\circ \)

2. **Use the relationship between the components:**
The relationship between the vertical component (Bv) and the horizontal component (Bh) is given by:
\[ \tan(\delta) = \frac{B_V}{B_H} \]
Rearranging this gives:
\[ B_V = B_H \cdot \tan(\delta) \]

3. **Calculate \( \tan(60^\circ) \):**
We know that:
\[ \tan(60^\circ) = \sqrt{3} \approx 1.732 \]

4. **Substitute the values into the equation:**
Now substitute \( B_H \) and \( \tan(60^\circ) \) into the equation for \( B_V \):
\[ B_V = 0.35 \times 10^{-4} \, T \cdot \sqrt{3} \]
\[ B_V = 0.35 \times 1.732 \times 10^{-4} \, T \]

5. **Calculate the value:**
Performing the multiplication:
\[ B_V \approx 0.6062 \times 10^{-4} \, T \]

6. **Round off the answer:**
Rounding off gives:
\[ B_V \approx 0.61 \times 10^{-4} \, T \]

### Final Answer:
The value of the vertical component of Earth's magnetic field is approximately \( 0.61 \times 10^{-4} \, T \).

---