capacitor.py

from integrator import RombergIntegrator as integral
import math


def d_field(rx,ry,rz,Q):
    den = rx**2 + ry**2 + rz**2
    if den == 0:
        return 0

    return Q * rz / math.pow(den, 1.5)


def I_x(x, ry, rz, Q, L):

    def ix(rx):
        return d_field(rx,ry,rz,Q)

    return integral(ix, x-L, x+L, precision = 1e-2)

def E_z(x,y,rz, Q = 1, L = 10):

    def iy(ry):
        return I_x(x,ry,rz,Q,L)

    return integral(iy,y-L, y+L, precision = 1e-2)


def V(x,y, z0 = 1, Q = 1, L = 10):
    def vz(rz):
        return 2*E_z(x,y,rz,Q, L)
    return integral(vz,0,2*z0,precision = 1e-2,silent = False)


distance = 0.1


potential = V(0,0,distance)
theory = distance*8*math.pi
print("In the center : potential = {} - theory = {};  diff = {:.2f}%".format(potential,theory, 200*(potential-theory)/(potential + theory)))


potential = V(10,10,distance)
print("In the corner : potential = {} - theory = {};  diff = {:.2f}%".format(potential,theory, 200*(potential-theory)/(potential + theory)))