Calculations for accelerating particles in a Cyclotron

[sss1]

Homework Statement

Picture

Relevant Equations

mv^2/2, f=qB/2pim

For this question part d, KE=mv^2/2=q^2B^2r^2/2m (I rearranged B=mv/qr for v and subbed into mv^2/2). q^2b^2r^2/2m=2F_cyc^2r^2m(pi)^2
But when I subbed the values in I got 16.45MeV but the answer says 165keV instead. I'm not sure what went wrong?

What's a good explanation for part e also?

 

[Steve4Physics]

But when I subbed the values in I got 16.45MeV but the answer says 165keV instead. I'm not sure what went wrong?

I got the same answer as you. (Except I rounded mine to an appropriate number of significant figures!)

It looks like the official answer is wrong - probably because whoever did it used r =53mm instead of r=53cm.

What's a good explanation for part e also?

As you probably know, ther rules here require you to show your own thoughts/attempt before guidance is offered.

 

[sss1]

As you probably know, ther rules here require you to show your own thoughts/attempt before guidance is offered

Well if the e field is strong, it’ll only take a few cycles until the particle leaves? Whereas if if the e field is weak, it’ll take a long time to leave the cyclotron, so the KE is the same regardless?

 

[kuruman]

Well if the e field is strong, it’ll only take a few cycles until the particle leaves? Whereas if if the e field is weak, it’ll take a long time to leave the cyclotron, so the KE is the same regardless?

You need to do better than that. What is an expression for the kinetic energy of the particle just before it exits? Is there an $E$ in it?