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.

 

[m2003]

I would like to commend you on your attempt at solving this problem. Your answers seem to be correct for the most part. Here are some additional explanations and calculations that may help you better understand the concepts involved in this problem:

1. Based on the information provided, the particle will indeed be moving into the page in a helical shape. This is because the force experienced by a charged particle in a magnetic field is perpendicular to both the velocity of the particle and the direction of the magnetic field. This results in circular motion, which in this case is tilted at an angle of 53 degrees to the +x-axis.

2. Your calculation for the work done on the particle is correct. Just to clarify, the unit for work is Joules (J), not Coulombs (C).

3. To calculate the velocity of the particle as it enters the magnetic field, we can use the formula for centripetal force: F = mv^2/r. In this case, the centripetal force is provided by the magnetic force (qvB), so we can equate the two and solve for v. This gives us v = (qBr/m)^(1/2). Plugging in the given values, we get v = 9.29 x 10^5 m/s, which is the same value you obtained.

4. The radius of the path in the magnetic field can be calculated using the formula r = mv/qB. This is the same formula you used, but just to clarify, the mass and charge used in this formula should be the actual mass and charge of the particle, not the mass and charge of a proton. In this case, the mass and charge of the particle are not specified, so we cannot calculate the exact value. However, if we assume that the particle is a proton (which seems reasonable given the context of the problem), we can use the values for the mass and charge of a proton to get an approximate value for the radius. This gives us r = 6.46 x 10^-3 m, which is the same value you obtained.

5. The period of motion can be calculated using the formula T = 2πm/qB. Again, the mass and charge used in this formula should be the actual values for the particle. Assuming the particle is a proton, we can plug in the values and get T = 4.37 x 10^-8 s, which is the