An electron and a proton enter a magnetic field with equal velocities. The particle that experiences more force is

Options

A. electron
B. proton
C. both experience same force
D. it cannot be predicted.

Answer

To solve the problem of determining which particle, an electron or a proton, experiences more force when entering a magnetic field with equal velocities, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Force on a Charged Particle in a Magnetic Field**:
The force \( F \) experienced by a charged particle moving in a magnetic field is given by the formula:
\[ F = Q \cdot v \cdot B \cdot \sin(\theta) \]
where:
- \( F \) is the magnetic force,
- \( Q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.

2. **Identify the Charges of the Particles**:
- The charge of an electron \( (Q_e) \) is approximately \( -1.6 \times 10^{-19} \) C (negative charge).
- The charge of a proton \( (Q_p) \) is approximately \( +1.6 \times 10^{-19} \) C (positive charge).

3. **Assume Equal Velocities and Magnetic Field**:
According to the problem, both the electron and proton enter the magnetic field with equal velocities \( v \) and are subjected to the same magnetic field strength \( B \).

4. **Assume the Angle**:
For maximum force, we can assume that the angle \( \theta \) is \( 90^\circ \), which means \( \sin(90^\circ) = 1 \). Thus, the formula simplifies to:
\[ F = Q \cdot v \cdot B \]

5. **Calculate the Forces**:
- For the electron:
\[ F_e = Q_e \cdot v \cdot B = (-1.6 \times 10^{-19}) \cdot v \cdot B \]
- For the proton:
\[ F_p = Q_p \cdot v \cdot B = (1.6 \times 10^{-19}) \cdot v \cdot B \]

6. **Compare the Magnitudes of Forces**:
The magnitudes of the forces are:
- \( |F_e| = 1.6 \times 10^{-19} \cdot v \cdot B \)
- \( |F_p| = 1.6 \times 10^{-19} \cdot v \cdot B \)

Since both forces have the same magnitude but opposite directions (due to the opposite charges), the absolute values of the forces are equal.

7. **Conclusion**:
Both the electron and the proton experience the same magnitude of force when entering the magnetic field with equal velocities.

### Final Answer:
Both the electron and the proton experience the same force.