Calculate the electric field induced from a spherical uniform charge distribution

electric_field_sphere.py

#-*- coding:utf-8 -*-
import random
import math
from functools import  reduce

def random_point_in_sphere(r):
	while True:
		x = random.uniform(-r, r)
		y = random.uniform(-r, r)
		z = random.uniform(-r, r)
		if x*x + y*y + z*z <= r*r:
			return (x, y, z)

def calcu_field(pointNum, sphereR, target):	
	points = [random_point_in_sphere(sphereR) for i in range(0, pointNum)]

	Ex, Ey, Ez = 0, 0, 0
	for point in points:
		x, y, z = map(lambda a, b: a - b, target, point)
		d2 = x*x + y*y + z*z
		d = math.sqrt(d2)
		E = k * q / d2
		Ex += E * x / d
		Ey += E * y / d
		Ez += E * z / d
	return Ex, Ey, Ez


# Coulomb's constant 8.987 * 10 ** 9 (N*m^2/C^2) in real world
k = 1

# magnitude of electric charge per point (in Coulomb)
q = 1

# radius of the spherical uniform charge distribution
a = 50

# location of the target
targetX = 30
targetY = 0
targetZ = 0

# number of the point with charge
pointNum = 100000

target = (targetX, targetY, targetZ)
r = math.sqrt(reduce(lambda x, y: x + y**2, (0,) + target))
if r < a:
	EFormula = k * pointNum * q / a / a / a * r
else:
	EFormula = k * pointNum * q / r / r

for i in range(0, 1):
	print('Calculation:', calcu_field(pointNum, a, target))
print('Formula:', EFormula)