The storms over Lakeview have gotten worse, with an almost permanent pitch black cloud system hovering overhead. A new model for the thundercloud needs to be produced to obtain a better understansding of how it is functioning. While they greatly appreciated the model you created last week for the Mapping N$\vec{E}$twork Sensory Array (MNSA), the data they are collecting from the sensors are simply not matching the model's predictions. They have concluded that modeling storm clouds as point charges was, in fact, problematic. Based on some research from the National Weather Service, it looks like a better model for clouds would be two flat sheets of charge since the negative charges in the cloud collect on the bottom of the cloud and the positive charges collect near the top.

Given that the negative charge is much closer to the ground (and headquarters), the Lakeviewians want to prioritize what the Mapping N$\vec{E}$twork Sensory Array (MNSA) around HQ will show based on the bottom of the cloud. (If you have time though, they'd be interested in whether the top of the cloud has any effect.) They have shared their model of the bottom of the most recent storm cloud (which is thankfully fully functioning, well-commented code), but they are having trouble getting the electric field on the ground. The Lakeviewians have asked your team for your help completing the code.

#Set up of the objects
ground = box(pos = vec(0,0,0), width=5000, length=5000, height=0.1, color=color.green)
mountains = [cone(pos=vec(-1800,0,0), axis=vec(0,1000,0), radius=700, color=vec(1,0.7,0.2)),
            cone(pos=vec(-1800,0,-1600), axis=vec(0,1000,0), radius=700, color=vec(1,0.7,0.2)), 
            cone(pos=vec(-1800,0,1600), axis=vec(0,1000,0), radius=700, color=vec(1,0.7,0.2))]
HQ = box(pos = vec(-100,100,0), width = 15, length = 15, height= 200, color = color.blue)
cloud = box(pos = vector(0,1000,0), size = vector(500, 1, 500), color = color.white)


#Lines 13-48 create a grid of spheres to represent the bottom of the cloud (this part of the code doesn't need be modified):

#Define how many chunks to split the cloud in the x direction (define x size of the cloud grid)
nx = 10
#Define how many chunks to split the cloud in the z direction (define z size of the cloud grid)
nz = 10

#Define where the cloud should start/stop in the x direction
startx = -250
endx = 250
#Define the spacing between each chunk in the x, based on where the cloud start/stops and how many chunks there are
stepx = (endx - startx)/nx

#Define where the cloud should start/stop in the z direction
startz = -250
endz = 250
#Define the spacing between each chunk in the z, based on where the cloud start/stops and how many chunks there are
stepz = (endz - startz)/nz

#Create an empty list to store each cloud chunk
listOfCloudChunks = []

#For each cloud chunk in the x-direction
for i in range(0,nx):
    
    #Define the x-location of the cloud chunk
    xloc = startx + i*stepx
    
    #For each cloud chunk in the z-direction
    for j in range(0,nz):
        
        #Define the z-location of the cloud chunk
        zloc = startz + j*stepz
    
        #Make a sphere at that x-z location
        cloudChunk = sphere(pos = vector(xloc,1000,zloc), radius = 50, color = color.red)

        #Add the sphere to the list of cloud chunks (so we can use it later)
        listOfCloudChunks.append(cloudChunk)

#This part needs to be fixed and commented...
obsLocation = vector(0,0,0)
Enet = vector(0,0,0)


Q = -15
dQ = Q/(nx*nz)
k = 9e9


for chunk in listOfCloudChunks:
    
    Enet = vector(0,0,0)

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.

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 charges 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)     

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)