Cyclotron is used to accelerate

Options

A. (a) Only negatively charged particles
B. (b) neutron
C. (c) Both positively and negatively charged particles
D. (d) Only positively charged particles

Answer

To solve the question regarding the use of a cyclotron in accelerating charged particles, we can break down the explanation step by step.

### Step-by-Step Solution:

1. **Understanding the Cyclotron**: A cyclotron is a type of particle accelerator that uses a magnetic field and an electric field to accelerate charged particles to high speeds.

2. **Nature of Charged Particles**: Charged particles can be either positively charged (like protons) or negatively charged (like electrons). The question asks which type of charged particles a cyclotron can accelerate.

3. **Principle of Operation**: The cyclotron operates on the principle that the magnetic force acting on a charged particle provides the necessary centripetal force to keep the particle moving in a circular path. The magnetic force \( F_m \) is given by:
\[ F_m = B \cdot q \cdot v \]
where \( B \) is the magnetic field strength, \( q \) is the charge of the particle, and \( v \) is its velocity.

4. **Centripetal Force**: The centripetal force \( F_c \) required to keep the particle in circular motion is given by:
\[ F_c = \frac{m \cdot v^2}{r} \]
where \( m \) is the mass of the particle, \( v \) is its velocity, and \( r \) is the radius of the circular path.

5. **Equating Forces**: For the cyclotron to work, the magnetic force must equal the centripetal force:
\[ B \cdot q \cdot v = \frac{m \cdot v^2}{r} \]

6. **Solving for Velocity**: Rearranging the equation gives us an expression for the velocity \( v \):
\[ v = \frac{q \cdot B \cdot r}{m} \]
This shows that the velocity of the charged particle increases as the radius \( r \) increases.

7. **Conclusion**: Since the cyclotron can accelerate both positively and negatively charged particles, the correct answer to the question is that the cyclotron is used to accelerate both positively and negatively charged particles.

### Final Answer:
The cyclotron is used to accelerate **both positively and negatively charged particles**.