184_projects:f21_project_5

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

#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)

#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

# 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
Evector=arrow(pos=rpoint, axis=scale*Enet, color=color.orange, shaftwidth=apoint.radius/2)