exercises by lookang: adapted from http://webphysics.davidson.edu/physlet_resources/bu_semester2/c13_cyclotron.html
The building of the cyclotron model is based on a optional activity in http://www.opensourcephysics.org/items/detail.cfm?ID=8984 Charge in Magnetic Field Model written by Fu-Kwun Hwang edited by Robert Mohr and Wolfgang Christian
The learning from this optional activity demonstrate student's learning in performance tasks. 5 stars!
There are many activities that can be design in this simulation.
refer to http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1972.0 for Charge Particle in Magnetic Field B Java Applet in 3D
Prior Knowledge required
charged particles
electric field & magnetic field
Engage
1. Early years scientists accelerate particle in linear accelerators but they face a problem of the need for a long linear path to accelerate the particle. Can you think of a way to reduce the need for a long path?
hint: look at the running track of a stadium, can you think of a way to
bend the particle with the magnetic field and accelerate with electric
field?
Stadium image by jjjj56cp, licensed under Creative Commons Attribution 2.0 Generic
After some discussions, students can share their ideas through oral/verbal presentation.
Teacher can praise some of the ideas and point them to Ejs as a means to test out their ideas using this Ejs simulation codes as templates for implementation.
Explore
1. Explore the simulation, this simulation is designed with a charge particle in a system of magnetic fields in z direction.
2 The play button runs the simulation, click it again to pause and the reset button brings the simulation back to its original state.
3 select Bz =0 (key in the value 0 follow by "enter" on keyboard), Ey =0, vy = 60, and play the simulation. Notice that the path of the particle in a straight line in the y direction. What is the physics principle simulatted here.
hint: newton's 1st law
4 reset the simulation.
5 using the default values(Bz =1, Ey=0, Vy=60), play the simulation. what did you observe? explain the motion in terms of the influences of magnetic field (assume gravitational effect can be neglected)
6 explore the slider x, y, and z. what do these sliders control?
7 explore the slider vx, vy, and vz. what do these sliders control?
8 by leaving the cursor on the slider, tips will appear to give a description of the slider. you can try it the following sliders such as the charge q, mass m, radius of dee(magnets) R.
9 there are some values radius of circular path r, kinetic energy of particle KE, resultant velocity vr and resultant force F on the m.
10 vary the simulation and get a sense of what it does.
11 reset the simulation
12 using the values(Bz =1, Ey=0, Vy=60, Ey =10. observe the difference in the introduction of Ey in the gaps.
13 notice that the Ey field is alternating, explain the purpose of this Ey in this simulation.
14 propose the logic deployed by this simulation to time the switching of Ey. Can you think of other swtiching logic?
15 note the first time the charge crosses the whole gap its kinetic energy increases by an amount ΔK. determine this value from looking at the value bar of KE, you may select the checkbox to view the scientific graph of KE vs t.
answer: 2421.4-2021.5 = 399.9 ≈ 400 J
16What is the change in kinetic energy associated with just moving in each half-circle in a dee (the magnetic field).
hint: look at the value bar of KE, you may select the checkbox to view the scientific graph of KE vs t.
Explain:
16 explain why this it is so?
hint: In the dee(magnetic field) the force on the charge comes from the magnetic field, so the force is perpendicular to the velocity. The speed, and hence the kinetic energy, stays constant, so the change is zero.
17 The first time the charge crosses the gap its kinetic energy increases by an amount ΔK say 400 J. Assuming the electric field in the gap is the same magnitude at all times but in opposite direction to earlier time, what is the change in kinetic energy the second time the charge crosses the gap?
hint: 2819.5-2421.4 = 398.1 ≈ 400 J
Elaborate
18 suggest with reason why the values for 15 and 17 are not exactly the same
hint: look at the value of vx
answer: the exiting from magnetic field causes the vx to be slightly bigger than 0, thus the resultant velocity is increased very slightly.
Evaluate:
19 A scientist ask a question "To increase the speed of the particles when they emerge from the cyclotron. Which is more effective, increasing the electric field Ey=-Vy/dy across the gap or increasing the magnetic field Bz in the dees? " play the simulation for different initial condition and design an experiment with tables of values to record systematically, determine what is the more "effective" method. State your assumptions made.
hint: assumption is outside physical radius of dee = R is fixed.
the start velocity vy =0
the start x = 0
Note that whatever the magnitudes of the fields the final half-circle the charge passes through in the dee has a radius approximately equal to R, the radius of the dee itelf. The radius of the circular path of a charged particle in a magnetic field is:
N2L: F = ma
circular: v.B.q = m.v^2/r
r = mv/Bq.
In this case the speed of the particle is RBq/m = v
Therefore the final kinetic energy is:
KE = 1/2 mv2 = 1/2. m. (RBq/m)^2 = 1/2. R^2q^2B^2/m
Have Fun!
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