Your team has been hired as part of a larger team that is developing a micro-particle accelerator. Your team is tasked with modelling 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.

R = 0.02
Q = 1e-9 
N = 20

myring = ring(pos = vector(0,0,0), radius = R, axis = vector(0,0,1), color = color.blue, thickness = 0.02*R)

oofpez = 9e9 #1/(4pi epsilon_0) in N m^2/C^2
dq = Q/N #charge of a piece

Enet = vector(0,0,0) #net electric field of all pieces

scale=1e-5

ObsList = []

phi = 0
dphi = pi/4


point = sphere(pos = vector(0,0.01,0.05), color = color.red, radius = R/40)
rpoint = point.pos #location of the point in space to calculate E field
    
dtheta = 2*pi/N #theta increment for our loop
theta = dtheta/2 #initial theta for first piece of loop
    
while theta<2*pi:
    
    rpiece = R*vector(cos(theta),sin(theta),0) #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 due to piece at rpoint
    Enet = Enet + dE #net electric field of the first one up to this one
        
    particle = sphere(pos = rpiece, radius = 2*point.radius, color = color.yellow) 
        
    theta = theta + dtheta
        
Evector = arrow(pos = rpoint, axis = scale*Enet, color = color.orange)      

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)