Question

In cyclotron the resonance condition is:
A. The frequency of revolution of charged particles is equal to the frequency of A.C. voltage sources.
B. The frequency of revolution of charged particles is equal to the frequency of applied magnetic field.
C. The frequency of revolution of charged particles is equal to the frequency of rotation of earth.
D. The frequency of revolution of charged particle, frequency of A.C. source and frequency of magnetic field are equal

Answer 1

Hint: A charge particle behaves in the presence of electric and magnetic fields. Learn the concepts of cyclotron and study what principle it uses to accelerate the charge particles inside it. Compare the cyclotron frequency and the frequency of the voltage applied to find the resonance condition.

Complete Step-by-Step solution:
The cyclotron is a machine that accelerates charged particles or ions to energies using magnetic and electric fields. The cyclotron uses the combination of both electric and magnetic fields. Since, the fields are perpendicular to each other they are called crossed fields.
The cyclotron uses the principle that the frequency of revolution of the charge particles does not depend on its energy.
In the cyclotron we have two semi-circular disk-like metal containers which are called the dee. Inside the metal container the electric field can’t act on the charged particle but the magnetic field moves the charged particle in a circular path inside the dee. When the particle moves from one die to the other electric field accelerates the charge particle.
The cyclotron frequency is expressed by the equation,
${{\nu }_{c}}=\dfrac{qB}{2\pi m}$
Where, q is the charge, B is the magnetic field and m is the mass of the particle.
Now, we apply the A.C. voltage with a frequency ${{\nu }_{a}}$ , which is adjusted such that the polarity of the dee is reversed in the same time as the time taken by the charged particle to complete half its rotation.
This requirement ${{\nu }_{a}}={{\nu }_{c}}$ is called the resonance condition of a cyclotron.
The correct option is (A).

Note: The change in polarity of the dee means that the sign of the electric field in the dee changes with the revolution of the charge to ensure that the charge is always accelerating inside the dee to obtain the charge particle with the highest velocity.