Duration: 1:32

37 views

0

In the given figure of a cyclotron, showing the particle source \( \mathbf{S} \) and the dees. A uniform magnetic field is directed up from the plane of the page. Circulating protons spiral outward within the hollow dees, gaining encrgy every time they cross the gap between the dees.
Suppose that a proton, injected by source \( S \) at the centre of the cyclotron in Fig., initially moves toward a negatively charged dee. It will accelerate toward this dee and enter it. Once inside, it is shielded from electric field by the copper walls of the dee; that is the electric field does not enter the dee. The magnetic field, however, is not sereened by the (nonmagnetic) copper dee, so the proton moves in circular path whose radius, which depends on its speed, is given by
For a given charge particle a cyclotron can be "tune" by :
DV
(A) changing applied A.C. voltage only difference between the dees is reversed. Thus, the both
proton again faces a negatively charged dee and is
(C) changing applied magnetic field only negatively charged dee and is again accelerated. This
(D) by changing frequency of applied A.C.
process eontinest the eirculating pron atways being in step, with the osemations or the dee potential, unti system. There a deflector plate sends it out through a portal.

The key to the operation of the cyclotron is that the frequency \( f \) at which the proton circulates in the field (and that does not depend on its speed) must be equal to the fixed frequency \( \mathrm{f} \) _ of the electrical oscillator, or \( f=f \) (resonance condition).
(2)
This resonance condition says that, if the enerery of the circulating proton is to increase, cnerey must be fed to it at a frequency \( f_{\text {_. that is equal to the natural }} \) frequency \( f \) at which the proton circulates in the magnetic field.
Combining Eq. 1 and 2 allows us to write the resumance
condition as
\( \mathrm{qR}=2 \mathrm{rmf} \)
Physics walle
For the proton. 9 and \( m \) are fixed. The oscillator (we assume) is designed to work at a single fixed trequency eq. 3 is satisfied and then many protons circulate. through the magnetic ficld, to cmerge as a bcam.
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live