Question

A charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes increase in its speed

• A. Only inside D₂
• B. Inside D₁, D₂ and the gaps
• C. Only inside D₁
• D. Only in the gap between D₁ and D₂

Answer 1

The Correct Option is D

Step 1: Basic Principle of Cyclotron:

A cyclotron is a device used to accelerate charged particles to high velocities using a high-frequency alternating electric field and a perpendicular magnetic field.

Important: The magnetic field inside the two hollow semi-circular electrodes (D-shaped chambers, called "Dees") only bends the path of the particle into a circular trajectory but does not increase its speed.

Step 2: Role of Electric Field:

The charged particle gains kinetic energy (and hence increases its speed) only when it crosses the gap between the two Dees, where a strong alternating electric field is applied.

This electric field accelerates the charged particle each time it crosses the gap, thus increasing its velocity.

Step 3: Clarification of given options:

• Inside Dees (D₁ and D₂): The particle moves under the influence of a uniform magnetic field. Hence, the speed remains constant inside each Dee.
• Between Dees (gap): A strong electric field exists in the gap. Hence, the particle accelerates (increases speed) here.

Thus, the charged particle accelerates (increases speed) only in the gap between the Dees.

Final Answer: Option (D) Only in the gap between \(D_1\) and \(D_2\) 

Answer 2

In a cyclotron, a charged particle undergoes acceleration in the presence of a magnetic field and a rapidly oscillating electric field (RFO - Radio Frequency Oscillator). The magnetic field causes the charged particle to move in a circular path, while the electric field provides the acceleration.

The electric field is only active in the gap between the two D-shaped electrodes, \( D_1 \) and \( D_2 \), which creates a potential difference that accelerates the charged particle.

- Inside \( D_1 \) and \( D_2 \), the charged particle does not experience any acceleration because the electric field is absent in these regions. Instead, the magnetic field forces the particle to move in a circular path, but this does not result in an increase in speed.
 
- The acceleration only occurs in the gap between the electrodes \( D_1 \) and \( D_2 \), where the charged particle experiences the electric field that increases its speed.

Thus, the correct answer is (D) – the particle only accelerates in the gap between \( D_1 \) and \( D_2 \).