Choose the wrong statements

Options

A. the radius of path of a charged particle moving in a uniform magnetic field is proportional to the momentum of the particle
B. an electron beam is moving towards east, on which a perpendicular magnetic field is acting upwards . The beam will be deflected towards the north direction
C. a positive charge is going straight away from the observer. The magnetic line of force produced due to it are in clockwise direction.
D. while passing through a given place , the path of electron remains straight line . It can be definitely said that the magnetic field is not present at that place

Answer

To solve the question of identifying the wrong statements regarding the behavior of charged particles in a magnetic field, we will analyze each statement step by step.

### Step 1: Analyze the First Statement
**Statement A:** "The radius of the path of the charged particle in a uniform magnetic field is proportional to the momentum of the particle."

- **Formula:** The radius \( r \) of the path of a charged particle moving in a magnetic field is given by the formula:
\[ r = \frac{mv}{qB} \]
where \( m \) is the mass, \( v \) is the velocity, \( q \) is the charge, and \( B \) is the magnetic field strength.
- **Analysis:** The momentum \( p \) of the particle is given by \( p = mv \). Thus, we can rewrite the radius as:
\[ r \propto \frac{p}{qB} \]
This shows that the radius is directly proportional to the momentum \( p \) of the particle. Hence, this statement is **correct**.

### Step 2: Analyze the Second Statement
**Statement B:** "An electron beam is moving towards the east on which a perpendicular magnetic field is acting upwards; the beam will be deflected towards the north direction."

- **Direction Analysis:**
- The electron is moving east, and the magnetic field is acting upwards (out of the plane).
- Using Fleming's Left-Hand Rule (for negative charges), we can determine the direction of the force acting on the electron.
- **Result:** The force will be directed towards the north. Therefore, this statement is also **correct**.

### Step 3: Analyze the Third Statement
**Statement C:** "The positive charge is going in a straight way from the observer; the magnetic field lines produced due to it are in the clockwise direction."

- **Direction Analysis:**
- For a positive charge moving straight away from the observer, we apply the Right-Hand Rule.
- If the thumb points in the direction of the charge's motion (away from the observer), the fingers curl in the direction of the magnetic field lines.
- **Result:** The magnetic field lines will be counterclockwise when viewed from the perspective of the observer. Thus, this statement is **incorrect**.

### Step 4: Analyze the Fourth Statement
**Statement D:** "While passing through a given place, if the path of the electron remains a straight line, it can be definitely said that the magnetic field is not present."

- **Analysis:**
- A charged particle can move in a straight line in a magnetic field if the velocity of the particle is parallel to the magnetic field (i.e., \( \vec{v} \) is parallel to \( \vec{B} \)).
- This means that the presence of a magnetic field does not necessarily imply that the path must curve.
- **Result:** Therefore, this statement is **incorrect**.

### Conclusion
The wrong statements are **C and D**.