Story of Flux and Ellipse

Electricity and Magnetism Level pending

A particle with charge q = + 10 q=+10 is position at N ( x , y , z ) = ( 0 , 0 , 1 ) N(x,y,z)=(0,0,1) at that orange dot as shown in figure. Find the flux passing through the green surface as shown in figure. Equation of ellipse is 4 x 2 + 9 y 2 = 36 4x^{2}+9y^{2}=36 . Details and assumptions 1) Electric permittivity ϵ 0 = 1 \epsilon_{0}=1


The answer is 0.303.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Steven Chase
Mar 16, 2020

Nice problem. Solution code is attached. 

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import math

#(x**2.0)/9.0 + (y**2.0)/4.0 = 1.0
#(x/a)**2.0 + (y/b)**2.0 = 1.0

N = 5000

a = 3.0
b = 2.0
R = 2.0

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

q = 10.0

xq = 0.0
yq = 0.0
zq = 1.0

e0 = 1.0

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

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

phi = 0.0

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

# Flux through green surface in 1st quadrant
# Multiply by four due to symmetry

dx = a/N

nx = 0.0
ny = 0.0
nz = -1.0

x = 0.0
z = 0.0

while x <= a:

    #(x/a)**2.0 + (y/b)**2.0 = 1.0

    right = 1.0 - (x/a)**2.0
    yf = b*math.sqrt(right)

    dy = yf/N

    dS = dx*dy

    y = 0.0

    while y <= yf:

        rsq = x**2.0 + y**2.0

        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

        if rsq > R**2.0:
            phi = phi + 4.0*dphi

        y = y + dy

    x = x + dx

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

print N
print ""

print phi

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


#1000

#0.303896016113
#>>> ================================ RESTART ================================
#>>> 
#2000

#0.303849491858
#>>> ================================ RESTART ================================
#>>> 
#5000

#0.3038216394
#>>>

1 Helpful 1 Interesting 3 Brilliant 0 Confused

@Steven Chase Sir I want know that you type this whole code in computer It's code of 112 lines. ?? Every time you make new code from starting.???

A Former Brilliant Member - 1 year, 2 months ago

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All of these problems are similar. So I just modify the code from the previous problem each time.

Steven Chase - 1 year, 2 months ago

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