Choose the wrong statement -

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 statement among the given options, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Analyze the First Statement:**
- The first statement claims that the radius of the path of a charged particle moving in a magnetic field is proportional to the momentum of the particle.
- The formula for the radius \( R \) of the path of a charged particle in a magnetic field is given by:
\[ R = \frac{mv}{qB} \]
where \( m \) is the mass, \( v \) is the velocity, \( q \) is the charge, and \( B \) is the magnetic field strength.
- Since momentum \( p \) is defined as \( p = mv \), we can rewrite the radius as:
\[ R \propto \frac{p}{qB} \]
- This shows that the radius is indeed proportional to the momentum of the particle.
- **Conclusion:** This statement is correct.

2. **Analyze the Second Statement:**
- The second statement describes an electron beam moving towards the east with a magnetic field acting upwards.
- Using the right-hand rule, the direction of the force on a negative charge (electron) can be determined.
- The force \( F \) on the charge is given by \( F = q(\mathbf{v} \times \mathbf{B}) \).
- Here, the velocity is towards the east and the magnetic field is upwards, which results in a force directed towards the north.
- **Conclusion:** This statement is also correct.

3. **Analyze the Third Statement:**
- The third statement states that a positive charge moving in a straight line from the observer produces magnetic lines of force in a clockwise direction.
- Using the right-hand rule, if the observer is looking at the positive charge moving away from them, the magnetic field lines will indeed appear to be in a clockwise direction.
- **Conclusion:** This statement is correct.

4. **Analyze the Fourth Statement:**
- The fourth statement claims that if an electron passes through a given place in a straight line, it can be definitively said that there is no magnetic field present at that location.
- This statement is misleading. An electron can move in a straight line even in the presence of a magnetic field if the magnetic force is balanced by another force, such as an electric field.
- Therefore, it is incorrect to assert that the absence of deflection implies the absence of a magnetic field.
- **Conclusion:** This statement is wrong.

### Final Answer:
The wrong statement is the **fourth statement**.

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