Flux in between Rings

Electricity and Magnetism Level pending

A particle with charge q = + 10 q=+10 is position at a point F F ( x , y , z ) = ( 1 , 2 , 3 ) (x,y,z)=(1,2,3) at that blue dot as shown in figure.Both orange and green circle are in X − Y X-Y plane and centered at orgin. The radius of orange and green circle are 2 2 and 1 1 respectively . Find the electric flux entering in the orange surface. Details and Assumptions

1) Electric permittivity ϵ o = 1 \epsilon_{o}=1


The answer is 0.405.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Steven Chase
Mar 14, 2020

Solution code attached: 

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import math

N = 5000

#####################################

q = 10.0

xq = 1.0
yq = 2.0
zq = 3.0

e0 = 1.0

#####################################

k = 1.0/(4.0*math.pi*e0)

phi = 0.0

#####################################
#####################################
#####################################
#####################################

# Disk 

dr = 1.0/N
dtheta = 2.0*math.pi/N

nx = 0.0
ny = 0.0
nz = -1.0

r = 1.0

while r <= 2.0:

    theta = 0.0

    while theta <= 2.0*math.pi:

        x = r*math.cos(theta)
        y = r*math.sin(theta)
        z = 0.0

        dS = r*dr*dtheta

        Dx = x - xq
        Dy = y - yq
        Dz = z - zq

        D = math.sqrt(Dx**2.0 + Dy**2.0 + Dz**2.0)

        ux = Dx/D
        uy = Dy/D
        uz = Dz/D

        E = k*q/(D**2.0)

        Ex = E * ux
        Ey = E * uy
        Ez = E * uz

        dot = Ex*nx + Ey*ny + Ez*nz

        dphi = dot * dS

        phi = phi + dphi

        theta = theta + dtheta

    r = r + dr

##################################################################

print N
print phi

#1000
#0.406294274148
#>>> ================================ RESTART ================================
#>>> 
#2000
#0.405865379244
#>>> ================================ RESTART ================================
#>>> 
#5000
#0.405516187402

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