In the previous problem, if `(phi)` is the angle between line of emergence DE and normal DF at point D, ratio of `(phi)//(theta)` for positive value of `(theta)` will be

Options

A. `1`
B. `gt1`
C. `lt1`
D. depands upon `vec(B)` and charge

Explanation

To solve the problem, we need to find the ratio of the angles \(\phi\) and \(\theta\) for a charged particle moving in a magnetic field, where \(\phi\) is the angle between the line of emergence DE and the normal DF at point D, and \(\theta\) is the angle of incidence with respect to the perpendicular CA drawn on line PQ.

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- We have a charged particle moving in a magnetic field, which follows a circular path. The radius of this circular path is given by \( R = \frac{MV}{QB} \), where \( M \) is the mass of the particle, \( V \) is its velocity, \( Q \) is the charge, and \( B \) is the magnetic field strength.

2. **Identifying Angles**:
- At point D, the line of emergence DE makes an angle \(\phi\) with the normal DF. The angle of incidence \(\theta\) is defined with respect to the perpendicular CA drawn on line PQ.

3. **Using Geometry**:
- In the circular motion of the particle, the trajectory creates right angles at various points. Specifically, we can identify that the angles formed by the radius at points D and the tangent at point D are right angles.

4. **Triangles and Similarity**:
- By analyzing the triangles formed in the setup, we can see that triangles O, P, and O' and triangles O, Q, and O' are similar due to the equal sides and angles. This similarity gives us relationships between the angles.

5. **Equating Angles**:
- From the similarity of triangles, we can conclude that the angle \(\phi\) at point D is equal to the angle \(\theta\) at point A. Thus, we have:
\[ \phi = \theta \]

6. **Finding the Ratio**:
- Therefore, the ratio of \(\phi\) to \(\theta\) is:
\[ \frac{\phi}{\theta} = 1 \]

### Final Answer:
The ratio of \(\phi\) to \(\theta\) for positive values of \(\theta\) is:
\[ \frac{\phi}{\theta} = 1 \]