The angle of dip at the poles and the equator respectively are

Options

A. `30^(@),60^(@)`
B. `0^(@),90^(@)`
C. `45^(@),90^(@)`
D. `90^(@),0^(@)`

Explanation

To find the angle of dip at the poles and the equator, we can analyze the behavior of the Earth's magnetic field at these two locations.

### Step-by-step Solution:

1. **Understanding the Angle of Dip**:
- The angle of dip (also known as magnetic inclination) is the angle made by the Earth's magnetic field lines with the horizontal plane.

2. **Analyzing the Poles**:
- At the North and South poles, the magnetic field lines are vertical. This means that the horizontal component of the magnetic field (B_H) is zero.
- Therefore, the vertical component (B_V) is equal to the total magnetic field (B).

3. **Using the Formula for Angle of Dip**:
- The formula for the angle of dip (θ) is given by:
\[ \tan \theta = \frac{B_V}{B_H} \]
- At the poles, since B_H = 0, we have:
\[ \tan \theta = \frac{B_V}{0} \]
- This results in:
\[ \tan \theta = \infty \]
- Therefore, θ at the poles is:
\[ \theta = \tan^{-1}(\infty) = 90^\circ \]

4. **Analyzing the Equator**:
- At the equator, the magnetic field lines are horizontal. This means that the vertical component (B_V) is zero.
- Thus, the total magnetic field (B) is equal to the horizontal component (B_H).

5. **Using the Formula for Angle of Dip at the Equator**:
- Again using the formula:
\[ \tan \theta = \frac{B_V}{B_H} \]
- At the equator, since B_V = 0, we have:
\[ \tan \theta = \frac{0}{B_H} \]
- This results in:
\[ \tan \theta = 0 \]
- Therefore, θ at the equator is:
\[ \theta = \tan^{-1}(0) = 0^\circ \]

6. **Final Answer**:
- The angle of dip at the poles is \(90^\circ\) and at the equator is \(0^\circ\).

### Summary:
- **Angle of dip at the poles**: \(90^\circ\)
- **Angle of dip at the equator**: \(0^\circ\)