# Homework Help: Particles in a Magnetic Field Question

1. Mar 14, 2017

1. The problem statement, all variables and given/known data
A beam of doubly ionized particles (i.e., twice the elementary charge) is accelerated across a potential difference of 2000 V in a mass spectrometer. They are then passed perpendicularly through a magnetic field of 0.085 T resulting in a radius of curvature 12.5 cm. Calculate the mass of the unknown ion.

2. Relevant equations
Fc= mv2/r
Fm= qvB
ΔV=ΔE/q

3. The attempt at a solution
We are supposed to derive a formula for q/m without velocity. I think the solution probably involves the centripetal force being equal to something but I'm not sure what. Any help would be appreciated, thank you!

2. Mar 14, 2017

### Staff: Mentor

In your third relevant equation, where does the ΔE end up?

3. Mar 14, 2017

ΔE is the change in potential energy experienced by the particle. I could find that, but I'm not sure what I would do from there.

4. Mar 14, 2017

### Staff: Mentor

How is the change in energy expressed by the particle?

5. Mar 14, 2017

Sorry, I'm not quite sure what you mean! To be honest I'm not even sure if I need that equation.

6. Mar 14, 2017

### Staff: Mentor

Oh, you definitely need it

What happens to a charged particle when it "falls" through a potential difference? What about the particle changes?

7. Mar 14, 2017

Haha ok good! I guess it gains kinetic energy and loses potential energy, would that ΔE be equal to 1/2mv2?

8. Mar 14, 2017

### Staff: Mentor

Why, yes it would!

9. Mar 14, 2017

Perfect! Ok, so I can say that ΔE= 6.4x10-16 J which would also equal 1/2mv2. After that I'm still not sure what to do!

10. Mar 14, 2017

### Staff: Mentor

You now have an expression involving m and v. What's another relationship that involves m and v once the particle enters the magnetic field?

11. Mar 15, 2017

Fc= mv2/r ?

12. Mar 15, 2017

### Staff: Mentor

Try it.

13. Mar 15, 2017

OH!! So I can say Vq= 1/2mv2 and mv2/r= qvB... So I solved for v on both sides and got v=qBr/m and v=√2Vq/m and then combine those, solve for q/m and so q/m=2V/B2r2! I plugged in the numbers and got the right answer, 9.0x10-27 kg. Thank you so much for your help, glad I finally got it :)

14. Mar 15, 2017

### Staff: Mentor

Well done! Glad I could help.