The angle of dip at a place is `40.6^(@)` and the intensity of the vertical component of the earth's magnetic field `V=6xx10^(-5)` Tesla. The total intensity of the earth's magnetic field `(I)` at this place is

Options

A. `7xx10^(-5)` tesla
B. `6xx10^(-5)` tesla
C. `5xx10^(-5)` tesla
D. `9.2xx10^(-5)` tesla

Answer

To find the total intensity of the Earth's magnetic field (I) at a place where the angle of dip is given, we can use the relationship between the vertical component of the magnetic field (V) and the total magnetic field intensity (I) with the angle of dip (θ).

### Step-by-Step Solution:

1. **Understand the relationship**: The vertical component of the Earth's magnetic field (V) is related to the total intensity (I) and the angle of dip (θ) by the formula:
\[ V = I \sin(\theta) \]

2. **Identify the known values**:
- Vertical component \( V = 6 \times 10^{-5} \, \text{Tesla} \)
- Angle of dip \( \theta = 40.6^\circ \)

3. **Rearranging the formula**: We can rearrange the formula to solve for the total intensity (I):
\[ I = \frac{V}{\sin(\theta)} \]

4. **Calculate \(\sin(40.6^\circ)\)**: Using a calculator or trigonometric table, we find:
\[ \sin(40.6^\circ) \approx 0.642 \]

5. **Substituting the values into the formula**: Now substitute the known values into the rearranged formula:
\[ I = \frac{6 \times 10^{-5}}{0.642} \]

6. **Perform the calculation**:
\[ I \approx \frac{6 \times 10^{-5}}{0.642} \approx 9.34 \times 10^{-5} \, \text{Tesla} \]

7. **Final result**: The total intensity of the Earth's magnetic field at this place is approximately:
\[ I \approx 9.34 \times 10^{-5} \, \text{Tesla} \]