In the above question, the pitch of the helix will be

A. 4.37 m
B. 0.437 m
C. 0.0437 m
D. 0.00437 m

Options

A. 4.37 m
B. 0.437 m
C. 0.0437m
D. 0.00437 m

Explanation

To find the pitch of the helix for a charged particle moving in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Pitch**:
The pitch of a helix is defined as the vertical distance traveled by the charged particle in one complete rotation around the magnetic field lines.

2. **Identify the Relevant Formula**:
The pitch \( P \) can be expressed as:
\[ P = V_{\parallel} \cdot T \]
where \( V_{\parallel} \) is the component of the velocity parallel to the magnetic field and \( T \) is the time period of one complete revolution.

3. **Determine the Time Period \( T \)**:
The time period \( T \) for a charged particle moving in a magnetic field is given by:
\[ T = \frac{2\pi m}{qB} \]
where:
- \( m \) is the mass of the charged particle,
- \( q \) is the charge of the particle,
- \( B \) is the magnetic field strength.

4. **Calculate the Velocity Component**:
The parallel component of the velocity \( V_{\parallel} \) can be expressed as:
\[ V_{\parallel} = V \cos \theta \]
where \( V \) is the total velocity of the particle and \( \theta \) is the angle between the velocity vector and the magnetic field direction.

5. **Substituting Values**:
Given values:
- \( V = 4 \times 10^5 \, \text{m/s} \)
- \( m = 1.6 \times 10^{-27} \, \text{kg} \)
- \( q = 1.6 \times 10^{-19} \, \text{C} \)
- \( B = 0.3 \, \text{T} \)
- Assuming \( \theta = 60^\circ \) (so \( \cos 60^\circ = 0.5 \))

First, calculate the time period \( T \):
\[ T = \frac{2\pi (1.6 \times 10^{-27})}{(1.6 \times 10^{-19})(0.3)} \]

Calculate \( V_{\parallel} \):
\[ V_{\parallel} = 4 \times 10^5 \times 0.5 = 2 \times 10^5 \, \text{m/s} \]

6. **Calculate the Pitch**:
Now substitute \( V_{\parallel} \) and \( T \) back into the pitch formula:
\[ P = V_{\parallel} \cdot T \]

After performing the calculations, you will find:
\[ P = 0.0437 \, \text{m} \]

7. **Select the Correct Option**:
From the options provided, the correct answer is:
**C. 0.0437 m**