biot-savart`s law problem

[별과바람]

# -*- coding: cp949 -*-

#작은 전류 요소에 의한 자기장

#저자: 

#날짜: 2016-12-01

 

from visual import *

scene.height = scene.width = 800

L = 5.e3

scene.range = L

 

#상수

m_const = 1.e-7 #자기 상수

 

#작은 전류 요소

 

source_current = 1.   #전류(암페어)

source_axis = vector(0, 0.01*L, 0) #dl 벡터

source_pos = vector(0,-10*L,0) #위치

curve(pos=[(0, -10*L, 0),(0, 10*L, 0)], color=color.green)#dl 방향 연장선

 

 

#관찰 위치

c_L=20*L

obs_radius = 0.0004*L #관찰 위치 반지름

d_theta = pi/3.

length = 2.*L #자기장을 그릴 전체 거리

obs_y = -10.*L #최초 관찰 위치 y 좌표

dy = c_L/1000.#관찰 위치 증가분

obs = [vector(0,-10*L,0)] #관찰 위치 리스트

obs1 = vector(0,-10*L,0)

while obs1.y < 10.*L:

    rate(100)

    obs1.y += dy

    obs.append( vector(0,obs1.y,0) )

 

 

 

#자기장  

scale_factor_m = 2.e-10 #자기장 화살표 스케일

m_field_origin = 0

i = 0

for hello in obs:

    r = hello - vector(obs_radius,0,0) #전류에서 보는 관찰 점의 상대 위치

    r_hat = r/mag(r) #상대위치의 단위 벡터

    m_field = m_const*source_current*dy*obs_radius/(mag(r)**3)#자기장

    m_field_origin += m_field

print "magnetic field by limited wire= ", m_field_origin

m_inf_field = 4.*pi*10**-7*source_current/(2.*pi*obs_radius)

print "magnetic field by infinite wire= ",m_inf_field

 

print "Done!!!"

I made this program that show biot-savart`s law. I think if obs_radius is much much smaller than c_L(wire total length), "magnetic field by limited wire " is same with  "magnetic field by infinite wire", but If i print this two result , "magnetic field by limited wire " is much bigger than "magnetic field by infinite wire". For example, If obs_radius is 0.00004*L, "magnetic field by limited wire " is 0.000250000004808 and  "magnetic field by infinite wire" is 1e-06. Why this problem happen?

(I use this formula)

[Bruce Sherwood]

The problem is that you divide the wire into segments dy = 100 long, but your observation location is only obs_radius = 2, so the numerical integration is very inaccurate. If you make obs_radius = 200, you get a result that is consistent with the analytical result. Note that your wire is 10000 long, so obs_radius = 200 is small compared with the length of the wire.

[별과바람]

Wow... I want this. Thank you!!