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:
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.
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
Those are the answers I got, Im not sure if they are completly wrong or right. I dont 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
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