Minimum time through a cyclotron

[kulgan]

Homework Statement

v initial is also equal to 1000

Homework Equations

?

The Attempt at a Solution

the only time the particle actually speeds up is during the crossing of the dees. so
integral of of Vdx = the maximum energy of the system, but i don't know how to make this into an equation that will give me minimum time.

any help would be great!

 

[tiny-tim]

welcome to pf!

hi kulgan! welcome to pf!

you need to add the time taken to go round those semi-circles …

that will depend on v and on the (constant) magnetic field B

 

[kulgan]

i understand that the time taken to go around each time is the same, so basically i need to find how many rotations it will take to get to the maximum speed that the cyclotron will support.
this brings me to my problem how do i get the amount of energy transferred by the dees each rotation.
the radius of the outside will determine my maximum speed correct?
so r=mv^2/qvb?
and how do i get the speed each dee imparts?

 

[tiny-tim]

… and how do i get the speed each dee imparts?

work done = qV ?

 

[kulgan]

(((qr²B²)/m)-500)/1000)+1 gives number of semi circle rotations.
time through a rotation is given by 2pi*r/v/2
so how do you determine the time through a rotation?
it should be the same time for each one but now I'm unsure how to determine what it should be...

 

[tiny-tim]

so how do you determine the time through a rotation?

from your equation r=mv²/qvb

 

[kulgan]

thanks for your help