The angular frequency of the charged particle in a cyclotron is

The correct answer is option 1) i.e. inversely proportional to its mass

CONCEPT:

• A cyclotron is a particle accelerator that accelerates charged particles to higher energies.
  • ​The working principle of a cyclotron is the Lorentz force.
  • The charged particle is placed at the center of the arrangement between the poles of two electromagnets.
  • The magnetic field causes the particle to trace a circular path as it experiences a Lorentz force.
  • An alternating voltage is applied across the setup, which further accelerates the particle.
• Lorentz force is the force experienced by electrically charged particles moving in a magnetic field.
  • The magnitude of the magnetic force (F) on a charge (q) moving at a speed (v) in a magnetic field of strength B is given by​

⇒ F = qvB

EXPLANATION:

• When a charged particle moves perpendicular to the magnetic field (θ = 90∘), it follows a curved path and undergoes circular motion.
• Here, the magnetic force supplies the centripetal force which keeps the particle in a circular motion.
• The centripetal force, 

​ ​

Where m is the mass of the particle, v is the velocity of the particle, and r is the radius of the circular path traced by the particle.

      ----(1)

• Angular velocity of the body is given as, 

​ 

Where r = radius and ω = 2πf, where f is the frequency.

Substituting (1) in the equation for ω,

• The angular frequency of the charged particle in a cyclotron is inversely proportional to its mass.