Proton Accelerator Homework Solutions

[nitrik]

Homework Statement

A proton accelerator, consisting of two charged plates whose potential difference is 45kV, is used to shoot a beam of protons into a magnetic field at an angle of 53 degrees to the +x-axis. The magnetic field is 1.5T, directed in the +x-direction

Below is an image:
http://img382.imageshack.us/img382/8806/bfieldsp0.jpg

1. Draw the path the beam takes in the B-field
2. Calculate the work done on q by the potential difference
3. Calculate the velocity of q as it enters the field
4. Calculate the radius of the path in the B-field
5. Calculate the period of motion of q in the B-Field
6. Calculate the pitch of the helix formed by q in the B-Field.

Homework Equations

F = qv x B
K.E = (1/2)mv^2
r = (mv)/(qB)
T = 2(pi)m/(qB)

The Attempt at a Solution

1. I am unsure, but using the right hand rule, will the particle be moving into the page, in a helical shape?

2. W = Q(V) = 1.6E-19 x 4.5E3 = 7.2 E-16 J

3. W = K.E, 7.2E-16 = (1/2)(m)(v^2), v = 928,587 m/s

4. F = ma
qvb = mv^2/r

v = r(w) (angular speed).. r = mv/qb = .00646 m

5. T = 2(pi)(m) / (qB) = 4.37E-8 s

6 ??

Those are the answers I got, I am not sure if they are completely wrong or right. I don't have a clue on how to calculate the pitch of the helix formeb by q in the B-field. I used the mass of a proton for m, and the change of a proton for q.

All help appreciated. thanks

 

[chaoseverlasting]

Your first three parts look ok. But in the 4th part, the velocity that you should take is that component which is perpendicular to the magnetic field. Thats why the particle follows a helical path cause one component of the velocity is completely unaffected.

Work out from there, you should get the rest.