Story of Sinx and Flux (part 2)

Electricity and Magnetism Level pending

A particle with charge q = + 10 q=+10 is position at N N ( x , y , z ) = ( 1 , 1 , 1 ) (x,y,z)=(1,1,1) at that orange dot as shown in figure. Find the flux through the surface area enclosed by two equation y = 0 y=0 and y = ∣ s i n x ∣ y=|sinx| ( 0 ≤ x ≤ 10 π ) (0≤x≤10π) for the five cycles only, from point A = ( 0 , 0 ) A=(0, 0) to B = ( 10 π , 0 ) B=(10π,0) . Point B B is not shown in figure because after that figure will be very large.

Details and Assumptions 1) For example if your answer comes 0.2300 like this then type your answer as 23. 2) Electric permittivity ϵ o = 1 \epsilon_{o}=1


The answer is 69.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Steven Chase
Mar 14, 2020

Nice problem. Simulation code below: 

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import math

N = 10000

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

q = 10.0

xq = 1.0
yq = 1.0
zq = 1.0

e0 = 1.0

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

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

phi = 0.0
S = 0.0

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

dx = 10.0*math.pi/N

nx = 0.0
ny = 0.0
nz = -1.0

x = 10.0**(-9.0)
z = 0.0

while x <= 10.0*math.pi:

    yf = math.fabs(math.sin(x))

    dy = yf/N
    dS = dx*dy

    y = 0.0

    while y <= yf:

        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
        S = S + dS

        y = y + dy

    x = x + dx

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

print N
print phi
print S

#>>> 
#1000
#0.690143433907
#20.0069914989

#>>> ================================ RESTART ================================
#>>> 
#2000
#0.690124877618
#20.0048624614

#>>> ================================ RESTART ================================
#>>> 
#5000
#0.690035077293
#20.0019121559
#>>>

#10000
#0.690022123909
#20.0009834197

1 Helpful 1 Interesting 1 Brilliant 0 Confused

@Steven Chase Sir I have reposted the problem https://brilliant.org/problems/story-of-sinx-and-flux/

A Former Brilliant Member - 1 year, 2 months ago

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Thanks, I solved that one too

Steven Chase - 1 year, 2 months ago

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