## Project 5

### Project 5A: Mini-Particle Accelerator

S.P.A.R.T.A.N force, still trapped in the town of Lakeview, has been sent as part of a larger governmental team to work on developing a micro-particle accelerator on the outskirts of town. Why does a town the size of Lakeview need a micro-particle accelerator? You are not at liberty to say. Your team is tasked with modeling the initial part of the accelerator, which uses a constant electric field to accelerate the charges. The concept is that the particles will enter a tube that is encapsulated by rings of charge. Your team needs to demonstrate that this concept will produce a *constant* electric field.

#### Part 1:

The first bit of code that you have received is from the previous team who were able to construct a single ring of charge and show the electric field due to that ring at some point. Your team should construct the electric field vectors for a circle inside the accelerator (smaller than the ring) at a distance of a few centimeters from the ring face.

GlowScript 2.7 VPython #Set up constants R = 0.02 r_obs = 0.05 Q = 1e-9 N = 20 dq = Q/N scale=1e-4 oofpez = 9e9 #1/(4pi epsilon_0) in N m^2/C^2 #Defining a ring at the origin myring = ring(pos = vector(0,0,0), radius = R, axis = vector(0,0,1), color = color.blue, thickness = 0.02*R) #Create an empty list for the charges ChargeList=[] #Set up the step size and angle for creating the charges dtheta = 2*pi/N theta = dtheta/2 #Create charges in a circle and add them to the ChargeList while theta < 2*pi: rpiece = R*vector(cos(theta),sin(theta),0) #location of piece particle = sphere(pos = rpiece, radius = R/20, color = color.yellow) ChargeList.append(particle) theta = theta + dtheta #Create an empty list for the observation points ObsList = [] #Set up the step size and angle for creating the observation points phi = 0 dphi = pi/4 #Create observation points in a circle and add them to the ObsList while phi < 2*pi: r_obs_piece = r_obs*vector(cos(phi),sin(phi),1) #location of piece obs_particle = sphere(pos = r_obs_piece, radius = R/20, color = color.red) ObsList.append(obs_particle) phi = phi + dphi #Find the electric field at each observation point for obs_point in ObsList: for charge in ChargeList: Enet=vec(0,0,0)

#### Part 2

After you got this initial code working, your team was able to construct a model of a tube consisting of multiple rings, all with the same charge. But, the field doesn't look quite right - it's not constant as expected. Your bosses seem to think the field can be made constant in the tube, so it's up to you to figure out how.

num_points = 10 num_rings = 11 N = 11 spacing = 0.02 # Set some constants and stuff R=0.02 #radius of ring in m ax = vector(0,0,1) # simplify things Q=1e-9 #charge of ring in C oofpez=9e9 #1/(4pi epsilon_0) in N m^2/C^2 #draw axis zaxis=cylinder(pos=-2*R*ax, radius=0.015*R, axis=4*R*ax, color=color.black) #draw points points = [] for i in range(num_points): xr = 0.01*sin(i*2*pi/num_points) yr = 0.01*cos(i*2*pi/num_points) points.append(sphere(pos=vector(xr,yr,0.01), color=color.red, radius=5*zaxis.radius)) #make and draw rings rings = [] ring_charge = [Q,Q,Q,Q,Q,Q,Q,Q,Q,Q,Q] for i in range(num_rings): loc = i - (num_rings)//2 rings.append(ring(pos=vector(0,0,spacing*loc), radius=R, axis=ax, color=color.blue, thickness=0.02*R)) # Find net field for apoint in points: Enet = vector(0,0,0) for i in range(len(rings)): aring = rings[i] # look at one ring dq = ring_charge[i]/N #charge of a piece dtheta = 2*pi/N #theta increment for our loop theta=dtheta/2 #initial theta for first piece of loop Ering = vector(0,0,0) #net electric field for single ring rpoint = apoint.pos scale=1.2*mag(rpoint)/8000 #used to scale the arrows representing E-field while theta<2*pi: rpiece = R*vector(cos(theta),sin(theta),aring.pos.z/R) #location of piece r = rpoint-rpiece #vector from piece to point in space rmag = mag(r) #magnitude of r rhat = norm(r) #unit vector for r dE = oofpez * dq / rmag / rmag * rhat # Electric field of peice of ring Enet = Enet + dE particle=sphere(pos=rpiece, radius=apoint.radius, color=color.yellow) #draw a particlee theta=theta+dtheta Evector=arrow(pos=rpoint, axis=scale*Enet, color=color.orange, shaftwidth=apoint.radius/2)