A particle of mass m, charge e and velocity v moving in a magnetic field B perpendicular to the motion of particle. The radius of its path is:

Options

A. `(Be)/(mv)`
B. `(ev)/(Bm)`
C. `(Bv)/(em)`
D. `(mv)/(Be)`

Explanation

To find the radius of the path of a charged particle moving in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Parameters**:
- Mass of the particle, \( m \)
- Charge of the particle, \( e \)
- Velocity of the particle, \( v \)
- Magnetic field strength, \( B \)

2. **Understand the Motion**:
- The particle is moving in a magnetic field that is perpendicular to its velocity. This means that the magnetic force will act as a centripetal force, causing the particle to move in a circular path.

3. **Apply the Formula for Radius**:
- The radius \( R \) of the circular path of a charged particle in a magnetic field is given by the formula:
\[ R = \frac{mv}{eB} \]
- Here, \( mv \) is the momentum of the particle, and \( eB \) is the magnetic force acting on the particle.

4. **Substitute the Values**:
- In this case, we directly substitute the known quantities into the formula:
\[ R = \frac{mv}{eB} \]

5. **Final Expression**:
- The final expression for the radius of the path of the particle is:
\[ R = \frac{mv}{eB} \]