Computational Exercise 3 : Cyclotron motion - Lab Report Example

Computational Exercise 3 Worksheet: Cyclotron motion What is cyclotron motion? (1pt) A charged particle is moving in the magnetic field with velocity. It moves in a circle at the end 2 Why does a charged particle moving in a direction perpendicular to a magnetic field move in a circle? (1pt)Taking the equation of, the cross product between will produce a perpendicular force for the magnetic field. 3 What is the force from the magnetic field on a charged particle moving parallel to a magnetic field?

What is the force on a charged stationary particle in a magnetic field? (1pt)forces on charged stationary particles will be 4 Write down the magnitude of the Lorentz force for a particle in a magnetic field. Write down the equation for the magnitude of the centripetal force. Set these two equations equal to each other, and solve for the radius. (1pt)5 After you get the code working (you can ask your instructor for guidance), save a screenshot which includes the particle trajectory. Try changing the charge strength, particle mass, and field strength one at a time.

Do these results agree with the equation you derived for the radius? Try it out and discuss what happened. Note: If the particle is much less massive, the code may stop working—decreasing the time step may help. Save a screenshot after making these changes. (2pts).Changing the charge strength, particle mass, and field strength gives results that agree with the equation derived. Increasing the charge strength, particle mass, and field strength one at a time resulted in a smaller radius while decreasing the charge strength, particle mass, and field strength one at a time resulted in a larger radius.

6 What happens if the particle is initially moving in the opposite direction? (1pt)If the particle is initially moving in the opposite direction, it will experience a force upwards. 7 Is it possible for the particle to travel such that it is un-deflected? If so, explain how and change the code to show that this is possible. What did you change? Save a screenshot. (3pts)It is possible for the particle to travel such that it is un-deflected. This is achieved by retaining the current magnetic field change and not changing it.

The scale was changed on the given Code. Introduction:(6pts)In this lab, we were simulating the motion of the charged particle. Cyclotron motion is an occurrence where a charged particle is moving in the magnetic field with velocity. It moves in a circle at the end. The charge strength, particle mass, and field strength could be changed. A similar experiment performed by J. J. Thomson in 1897 to measure the charge-to-mass ratio of the electron with incredible accuracy. In this experiment, a gas sample was introduced into the region existing between the charged plates and the flow of current was observed.

Thompson was able to prove that the cathode rays were produced from the cathode as a stream of negatively charged particles called electrons. He was able to determine the charge-to-mass ratio of the electron. Data sheets:Data sheet 1# charge moving in a magnetic field#from visual import *# set up scene for visualizationscene = display(width = 1024,height = 768, x=100, y=100, background = color.white, range=(1,1,1) )# designate visibility parameter 1 = Truearrowvis = 1# set position parametersxmax = .

5dx = xmax/5.# set up a set of locations to represent the B fieldgrid = []for x in arange(-xmax, xmax+dx, dx): grid.append(curve(pos=[(x,0,-xmax),(x,0,xmax)], color=(.6,.6,.6)))for z in arange(-xmax, xmax+dx, dx): grid.append(curve(pos=[(-xmax,0,z),(xmax,0,z)],color=(.6,.6,.6)))# set up B field representationB0 = vector(0,0.5,0)bfield=[]bscale = (xmax/3.)/mag(B0)for x in arange(-xmax, xmax+dx, 2*dx): for z in arange(-xmax, xmax+dx, 2*dx): bfield.append(arrow(pos=(x,0,z), axis=B0*bscale, color=(0,.8,.8)))## set up particle: place it inside or outside area of uniform B and designate charge## there are several cases to try:## (For example)## Outside: pos=(0.

75*xmax,dx,2*xmax), charge positive## Inside: pos=(-xmax/2.,dx,xmax/2.), charge positive## Outside: pos=(-0.75*xmax, dx ,2*xmax), charge negative## Inside: pos=(xmax/2.,dx, xmax/2. ), charge negative # Outside: pos=(xmax/2.,dx, 2*xmax - 3*dx), charge negative particle = sphere(pos=(xmax/2.,dx, 2*xmax - 3*dx), mass = 1.7e-27, charge= -1.6e-19, v = vector(0,1.e6,-1e7), color=(0,0,1), radius = dx/8, make_trail=True)# initial momentumparticle.

p = particle.mass*particle.v# set up an arrow to show force on the particlefarrow = arrow(pos=particle.pos, axis=(0,0,0), color=(0.6,0.6,0.6))# scale and visualize arrowfscale = 1.e11farrow.visible = arrowvis# set up an arrow to show velocity on the particlevarrow = arrow(pos=particle.pos, axis=(0,0,0), color=color.green)# scale and visualize arrowvscale = 1e-8varrow.visible = arrowvis# timedt = (xmax/(mag(particle.p)/particle.mass))/1000.scene.mouse.getclick()t = 0.# dynamics loop - motion of particle through B field# constrain motion to area of interestwhile particle.pos.z < xmax + 3.

1*dx and particle.pos.y < xmax: rate(500) # set up B field in a specific location and nowhere else if -xmax < particle.x < xmax and -xmax < particle.z < xmax: B = ### PHYSICS else: B = ### PHYSICS #### PHYSICS HERE ### # caculate velocity # calculate force # calculate momentum # calculate position #### PHYSICS HERE ### # update position and dimension of arrow farrow.pos = particle.pos farrow.axis = F*fscale varrow.pos = particle.

pos varrow.axis = particle.v*vscale #### update time ### Data sheet 2fscale=1.e11farrow.visible=arrowvis# set up arrow to show velocity on the particle varrow = arrow(pos= particle.pos, axis = (0,0,0), color=color.green) # scale and visualize arrowarrowvis = 1vscale=1e-8varrowcisible=arrowvis# timedt=(xmax/(mag(particle.p)/particle.mass))/1000scene.mouse.getclick()t=0# dynamic loop-motion of particle through B field #constrain motion to area of interest While particle.position.z