Calculating magnetic field to accelerate deutrons in a cyclotron

[sudipmaity]

Homework Statement

A cyclotron has oscillator frequency of 12×10^6 cycles /sec and dee radius 21 inches .Calculate the magnetic induction B needed to accelerate deutrons .
Given e=1.6 ×10^-19 coulomb and M (²₁H )=3.3×10^-27 kg.

Homework Equations

Frequency f= Bq/2πΜ

The Attempt at a Solution

Β=(2π×3.3 ×10^ -27 ×12 ×10^6)/1.6×10^ -19 = 1.55Wb/m².
Have i done this right? Why did they give me the dee radius if didn't need it?[/B]

 

[BvU]

Perhaps there was a part b) where they asked about the maximum speed the cyclotron can give the deuterons ?

 

[sudipmaity]

There is no part b.This is a past year university question.I don't have the answer to it.I will be grateful to you if you could verify my calculation.

 

[BvU]

PF isn't really meant to stamp-approve homework (would get us into trouble with all the teachers in the world). But in case this is self-study, I would say that, like you, I can't find much wrong with this straightforward calculation ...

The fun of a cyclotron is that at non-relativistic speeds the increase in speed causes the radius of the particle trajectories to increase, but the time to complete a revolution remains constant. The bigger the thing is, the more revolutions before spilling out, so the higher the kinetic energy reached, but that isn't part of the frequency / magnetic field relationship.

 

[sudipmaity]

Thank you.I never post homework questions. I post past year university question only.Our class is too overcrowded for the teachers to attend to individual doubts.Solving past year question gives a feel about the type of questions that can feature in an exam.

 

[BvU]

You're welcome. And practicing exercises is the best way to learn and to prepare for tests, exams and what have you.