Magnetic Line Integral (Part 3)

Electricity and Magnetism Level 5

A thin, infinitely long wire passes through the origin and is perpendicular to the x y xy plane. The conductor carries a current I I . Define two points in the x y xy plane.

C = ( 1 , 0 ) D = ( 2 , 1 ) C = (1,0) \\ D = (2,1) Define the following line integral, in which the path is a straight line from C C to D D :

∫ C D B ⋅ d ℓ = γ μ 0 I \int_C^D \mathbf{B} \cdot d \mathbf{\ell} = \gamma \, \mu_0 \, I What is the absolute value of γ \gamma ?

Notes:
- The symbol ( ⋅ ) (\cdot) denotes the vector dot product
- B \mathbf{B} denotes the vector magnetic flux density


The answer is 0.07379.

Steven Chase by Steven Chase , 37, USA

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1 solution

Steven Chase
Oct 28, 2019 
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import math

N = 10**6

Cx = 1.0
Cy = 0.0

Dx = 2.0
Dy = 1.0

dx = (Dx - Cx)/N
dy = (Dy - Cy)/N

I = 1.0
u0 = 1.0

Sum = 0.0


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

x = Cx
y = Cy

for j in range(0,N):

    r = math.hypot(x,y)

    ux = x/r
    uy = y/r

    vx = -uy
    vy = ux

    Bmag = u0*I/(2.0*math.pi*r)

    Bx = Bmag * vx
    By = Bmag * vy

    Sum = Sum + Bx*dx + By*dy

    x = x + dx
    y = y + dy



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

print math.fabs(Sum)
# 0.0737918724877

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