First slide

Force on a charged particle moving in a magnetic field

Question

Which of the following cyclotrons gives a proton beam of highest possible energy? The one having

Moderate

A

small Dees and weak magnetic field
B

small Dees and strong magnetic field
C

large Dees and weak magnetic field
D

large Dees and strong magnetic field

Solution

$r a d i u s o f t h e p a t h r = \frac{p}{q B} p i s t h e m o m e n t u m p = q B r k i n e t i c e n e r g y = \frac{p^{2}}{2 m} = \frac{q^{2} B^{2} r^{2}}{2 m}$

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