# How to find the speed of an ion using V, T, m, q?

1. Dec 17, 2012

### Apollinaria

Hello PF! How I've missed you! :)
Studying for a final that's in two days. Our prof skimped on the electricity/electron/unit thing. I don't even know what it's called!! :(

1. The problem statement, all variables and given/known data

I need to find the speed of an ion, as well as the magnitude of the magnetic force acting on it.

A Li+ ion,

m= 1.16E-26 kg
q= 1.60E-19 C
V (or EPE? Same thing?)= 400V
v= ?
B= 0.5 T

Is accelerated through a potential difference of 400V and enters a uniform magnetic field of 0.5T, perpendicular to the ion's velocity. Find v of the ion, find magnetic force acting on the ion.

2. Relevant equations

I'm given the formulas (on a magical exam formula sheet)
q=Ne
EPE=qV
E=( kq) / r^2
F= ( kq1q2 ) /r^2

3. The attempt at a solution

F=qE but don't have E....
F= qvBsin0 but don't have v.

Suggestions? I have a horrendous understanding of this unit... Our entire class is actually lost because of the lack of explanation on it :(

2. Dec 17, 2012

### Staff: Mentor

EPE is Electric Potential Energy. The units would be Joules. The potential difference through which the ion "falls" is 400V (Volts).

The unit "Volt" is equivalent to "Joules per coulomb". So if the ion with a charge of q= 1.60E-19 C falls through a 400V potential, what's the kinetic energy (Joules) it ends up with? Hint: you've listed an equation, EPE = qV, that is key (along with the relationship between work and energy).

3. Dec 17, 2012

### Apollinaria

Still not seeing where you're going with this.. I'm sorry, I'm terrible.
EPE= qV
= 1.6E-19 x 400V
= 6.4E-17 J

KE= 0.5mv2....

4. Dec 17, 2012

### Staff: Mentor

Yes, you're doing fine. By conservation of energy, the KE gained by the "falling" charge equals the change in potential energy. KE = EPE.

So solve for the velocity.

5. Dec 17, 2012

### Apollinaria

Thats exactly what I suspected but, starting with this

KEi + PEi + EPEi = KEf + PEf + EPEf

where does everything else go to leave me with KE and EPE? Kinetic because its falling...

Edit: Got the correct answer but still curious as to where the other energies disappeared to.

6. Dec 17, 2012

### Staff: Mentor

The problem statement makes no mention of gravity, so you're only dealing with Electrical Potential Energy here. So your PEi and PEf terms (presumably associated with gravitational potential) vanish. I used "falling" in quotes to denote that the charge is "falling" through an electrical potential difference, sorry if that was misleading

Dropping the PE terms from your expression,

KEi + EPEi = KEf + EPEf

KEf - KEi = EPEi - EPEf

ΔKE = ΔEPE

7. Dec 17, 2012

### Apollinaria

I apologize again for being so dense. Why is there a change in KE and EPE?

I'm usually better at this. I don't know whats wrong with me today!

8. Dec 17, 2012

### Staff: Mentor

The ion is moving through a potential difference, so there's a change in EPE (which, as you may recall, is position dependent on the location in a field). The ion is changing speed as it does so, so there's a change in KE. The change in KE balances the change in EPE. That's conservation of energy at work. Works for any conservative field, such as gravitational or electric fields.
Deep breaths, have some tea

9. Dec 17, 2012

### Apollinaria

Ooooooooooohhh. Now I get it! The more I look at these the more panicked I get. I have one day to finish my studies before the final :(