The factor(s) affecting the curvature of the trajectory of an electron moving in a magnetic field is -

Options

A. (a) charge
B. (b) magnetic field
C. (c) momentum
D. (d) All of these

Answer

To determine the factors affecting the curvature of the trajectory of an electron moving in a magnetic field, we can analyze the forces acting on the electron and how they relate to its motion.

### Step-by-Step Solution:

1. **Identify the Relevant Forces**:
- When an electron moves in a magnetic field, it experiences a magnetic force given by the equation:
\[ F = q(\mathbf{v} \times \mathbf{B}) \]
- Here, \( F \) is the magnetic force, \( q \) is the charge of the electron, \( \mathbf{v} \) is the velocity vector of the electron, and \( \mathbf{B} \) is the magnetic field vector.

2. **Magnitude of the Magnetic Force**:
- The magnitude of the magnetic force can be expressed as:
\[ F = B q v \sin \theta \]
- Where \( \theta \) is the angle between the velocity vector and the magnetic field vector.

3. **Factors Affecting the Force**:
- From the equation \( F = B q v \sin \theta \), we can see that the magnetic force depends on:
- The **charge** \( q \) of the electron.
- The **magnitude** of the magnetic field \( B \).
- The **velocity** \( v \) of the electron.
- The **angle** \( \theta \) between the velocity and the magnetic field.

4. **Relation to Curvature of the Trajectory**:
- The curvature of the trajectory of the electron is influenced by the magnetic force acting on it. The greater the force, the tighter the curvature.
- The centripetal force required for circular motion is provided by the magnetic force. Thus, we can relate the curvature (radius \( r \)) to the magnetic force:
\[ F = \frac{mv^2}{r} \]
- Setting the magnetic force equal to the centripetal force gives:
\[ B q v \sin \theta = \frac{mv^2}{r} \]
- Rearranging this, we can express the radius of curvature \( r \):
\[ r = \frac{mv}{B q \sin \theta} \]

5. **Conclusion**:
- From the above analysis, we conclude that the curvature of the trajectory of an electron in a magnetic field is affected by:
- The **charge** of the electron \( q \).
- The **magnitude** of the magnetic field \( B \).
- The **velocity** of the electron \( v \).
- The **angle** \( \theta \) between the velocity and the magnetic field.

Thus, the correct answer is that all of these factors affect the curvature of the trajectory of the electron.