Solve Velocity Selector: 750eV Electron & Cyclotron w/ 32.0MeV, 4.5T

[DFWDraco76]

I found an old post with an almost identical question: https://www.physicsforums.com/showthread.php?t=54092

However, I still don't see how to work the problem.

My question is phrased exactly the same, except B = 0.0170T and it's a 750eV electron.

I have absolutely no clue how I'm supposed to relate eV to velocity, but I'm pretty sure (at least I read it somewhere on the web) I should be able to set 1/2mv^2 = eV.

If I do this I end up with v = sqrt(2eV/m) = 4.06*10^16.

Plugging that into the equation E = vB = 6.90*10^14.

That's way off... The answer should be kV/m, and from various friends that have gotten it right I hear it should be 3 digits (i.e. 100 <= answer <= 999).

Can somebody give me a hint, help me along here?

EDIT: I have another question in which I need to somehow related eV to velocity as well. This one is finding the radius of a cyclotron, given it's to accelerate to 32.0 MeV using magnetic filed 4.5T. I know r = mv / qB, so once again I'm missing v.

 

[Hootenanny]

1/2mv^2 = eV.

Almost there; however, you need to convert the energy from eV to Joules before equating the formulae for kinetic energy. The effects of relativity are insignificant so you can still use the classical equation as you have done above.

 

[DFWDraco76]

Ok... So 1eV = 1.6*10^-19J
750eV*1.6*10^-19 = 1.2*10^-16 = j

v = sqrt(2j/m) = sqrt(2.4*10^-16 / 9.11*10^-31) = 1.623*10^7

still not right, is it?

 

[DFWDraco76]

never mind, I got it. thanks!