Question

A cyclotron operates with a given magnetic field and at a given frequency. If R denotes the radius of the final orbit, then the final particle energy is proportional to which of the following?

A. 1/RB. RC. R^2D. R^3E. R^4

Answer 1

The final particle energy in a cyclotron is proportional to the square of the radius of the orbit. The correct option is (C).

Step-by-step explanation:

The final particle energy is proportional to R²

In a cyclotron, the final particle energy increases as the radius of the orbit increases. The energy is proportional to the square of the radius (R²).

This is because the kinetic energy of a particle is given by KE = ½mv², and the velocity is directly proportional to the radius of the orbit (v = ωR, where ω is the angular velocity).

Therefore, the correct answer is Option C. R².

Answer 2

C. R^2

Step-by-step explanation:

A cyclotron is a particle accelerator which employs the use of electric and magnetic fields for its functioning. It consists of two D shaped region called dees and the magnetic field present in the dee is responsible for making sure the charges follow the half-circle and then to a gap in between the dees.

R is denoted as the radius of the final orbit then the final particle energy is proportional to the radius of the two dees. This however translates to the energy being proportional to R^2.