# Radius and period of charge in B field

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1. Apr 1, 2016

### velocity9

1. The problem statement, all variables and given/known data
A doubly charged helium atom (mass = 6.68 x 10-27 kg) is accelerated through a potential difference of 4.00x 103 V. What will be the radius of curvature of the path of the atom if it is in a uniform 0.460 T magnetic field?
Note: I hope this question is meant in advanced physics >.<
If not, I apologize. Please direct me towards the proper place.

2. Relevant equations
r = (mv)/(qB)

E = qV

K = ½mv^2

3. The attempt at a solution
I let
E=K and so
½mv^2 = qV
I solved for v which gave me
v = √((2*q*V)/m)
I subbed this v into
r = (mv)/(qB)

I know from the information provided that
B = 0.460 T
m = 6.68*10^-27 kg
V = 4.00*10^3
and I know q = 2*e
I also found v so there aren't any other unknowns, I subbed in...
I got 0.0199 m for r but my answer is said to be wrong. Not sure where I made a mistake. Any help is appreciated! Thank you

2. Apr 1, 2016

### TSny

Welcome to PF!

Your work looks correct. Maybe you made a mistake in plugging in the numbers. What did you get for the speed v?

3. Apr 1, 2016

### velocity9

I got 437740 m/s for the speed

4. Apr 1, 2016

### TSny

I think you might not have used the correct charge. Note that 2q = 4e.

5. Apr 1, 2016

### velocity9

gaah yes you are right! So sorry for the silly mistake. I had it written down correctly but my brain wouldn't convey the information to my fingers when plugging in to the calculator. Thank you so much for your time!!

6. Apr 1, 2016

### TSny

OK. Nice work!

7. Apr 1, 2016

### velocity9

For the second part of the question, it asks:
What is the period of revolution for the atom in the previous question?

I'm having a little bit of trouble deciding what is related to what. I figure I can use

ω = 2π/T

the velocity found.. that is ω, right?
Not sure how else they could be connected. I tried thinking in terms of centripetal velocity but that didn't get me anywhere.
Thank you in advance!

8. Apr 1, 2016

### Staff: Mentor

What's the length of the path that the atom follows? What's its speed around that path? How long does it take to cover that distance at that speed?

9. Apr 1, 2016

### velocity9

I know the velocity since I found it in the first part. I used
and found v = 6.19*10^5 m/s
I think the time to cover that distance would be the period. If I could find the distance, I could probably use simple v = d/t and rearranging for t=d/v, I think the units cancel to leave you with seconds which is the unit of period. I think.
The distance I'm kind of confused about. It's not simply the radius. I would look for a circumference or something of the sort but I'm not even sure the exact shape of the path. Do I need to know if it's a circle or something like that or am I going in the wrong direction again haha
Thank you for your time!

10. Apr 1, 2016

### Staff: Mentor

Well, you found a radius. What did you equate in order to find it? (What's it the radius of?)

11. Apr 2, 2016

### velocity9

Ok, so I found that mutiplying the d/v that we were discussing by 2pi works. I realize the units are convenient as we had discussed since all we are left with is seconds. I'm not entirely sure why the 2pi worked. I was searching about period and I noticed most of the periods had 2pi written next to them so I figured I would try but is it simply a matter of period having to be related with pi? Just trying to understand how my lucky guess worked. Thanks!

12. Apr 2, 2016

### Staff: Mentor

What is the relationship between the radius and circumference of a circle?

13. Apr 2, 2016

### velocity9

Thank you so much for your patience! It all makes sense now

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