Homogeneidad.ipynb

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  "metadata": {
    "colab": {
      "name": "Homogeneidad.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/fedemoss/HelmholtzCage/blob/main/Homogeneidad.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "07f9KQTDWFtI"
      },
      "source": [
        "**El objetivo de este código es estudiar la homogeneidad (H) para las bobinas circulares y cuadradas, en función de la dimensión de las bobinas y el punto de observación**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9WFSS5pkrR8r"
      },
      "source": [
        "import math\n",
        "import numpy as np\n",
        "from scipy.integrate import quad\n",
        "from numpy import sqrt, sin, cos, pi\n",
        "from matplotlib import pyplot as plt\n",
        "from scipy.optimize import curve_fit"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gx-F8VV5rWUk"
      },
      "source": [
        "## Constantes:\n",
        "## Todo está en SI\n",
        "\n",
        "N = 40  ## número de vueltas\n",
        "I = 1   ## corriente\n",
        "u0 = 1.256637062* 10 ** (-6)  ## permeabilidad magnética del vacio\n",
        "C = u0 * N * I / (4 * np.pi)  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wQ5u3MjKriwM"
      },
      "source": [
        "**DEFINICIÓN CAMPO DE JAULA CIRCULAR (B)**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SafErMVerZdl"
      },
      "source": [
        "## Término que aparece en común para todos los campos\n",
        "\n",
        "def terminoDivisorup(u, z, x, y, r, d):\n",
        "    return ((z + d/2)**2 + (x - r * cos(u))**2 + (y - r * sin(u))**2)**(3/2)\n",
        "  \n",
        "def terminoDivisordown(u, z, x, y, r, d):\n",
        "    return ((z - d/2)**2 + (x - r * cos(u))**2 + (y - r * sin(u))**2)**(3/2) \n",
        "\n",
        "## Campo en la dirección axial para las dos bobinas en cartesianas (Bz)\n",
        "\n",
        "def dBzup(u, z, x, y, r, d):\n",
        "    return C * r * (r - x * cos(u) - y * sin(u)) / terminoDivisorup(u, z, x, y, r, d)\n",
        "\n",
        "def dBzdown(u, z, x, y, r, d):\n",
        "    return C * r * (r - x * cos(u) - y * sin(u)) / terminoDivisordown(u, z, x, y, r, d) \n",
        "\n",
        "## Componente x del campo (par de bobinas)\n",
        "\n",
        "def dBxup(u, z, x, y, r, d):\n",
        "    return C * r  * (z + d/2) * cos(u)/terminoDivisorup(u, z, x, y, r, d)\n",
        " \n",
        "def dBxdown(u, z, x, y, r, d):\n",
        "    return C * r  * (z - d/2) * cos(u)/terminoDivisordown(u, z, x, y, r, d)\n",
        "\n",
        "## Componente y del campo (par de bobinas)\n",
        "\n",
        "def dByup(u, z, x, y, r, d):\n",
        "    return C * r * (z + d/2) * sin(u)/terminoDivisorup(u, z, x, y, r, d)\n",
        " \n",
        "def dBydown(u, z, x, y, r, d):\n",
        "    return C * r * (z - d/2) * sin(u)/terminoDivisordown(u, z, x, y, r, d)\n",
        "\n",
        "# Paper Restrepo: 'A comparative study of the magnetic field homogeneity for \n",
        "# circular, square and equilateral triangular Helmholtz coils'  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0SU-5g9HsLGc"
      },
      "source": [
        "**DEFINICIÓN DE CAMPO DE JAULA CUADRADA (B)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SUaOe55IrrM8"
      },
      "source": [
        "## Campo en el eje axial en cartesianas (Bz)\n",
        "## La expresión es muy grande por lo tanto la separamos en varias partes\n",
        "## bobinas a d/2 y -d/2 en el eje z con respecto al centro\n",
        "\n",
        "def SBz1up(z, x, y, l, d):\n",
        "    factorcomun = (x + l / 2)/((x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBz2up(z, x, y, l, d):\n",
        "    factorcomun = (x - l / 2)/((x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBz3up(z, x, y, l, d):\n",
        "    factorcomun = (y + l / 2)/((y + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((x - l /2) ** 2 + (y + l / 2) ** 2 + (z + d / 2) ** 2)     ## ojo acá\n",
        "    derecha = (l / 2 + x) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBz4up(z, x, y, l, d):\n",
        "    factorcomun = (y - l / 2)/((y - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((x - l /2) ** 2 + (y - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y - l / 2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "## Este es la función que importa\n",
        "\n",
        "def SBzup(z, x, y, l, d):\n",
        "    return SBz1up(z, x, y, l, d) - SBz2up(z, x, y, l, d) + SBz3up(z, x, y, l, d) - SBz4up(z, x, y, l, d)\n",
        "\n",
        "## Campo en el eje axial para la otra bobina\n",
        "\n",
        "def SBz1down(z, x, y, l, d):\n",
        "    factorcomun = (x + l / 2)/((x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBz2down(z, x, y, l, d):\n",
        "    factorcomun = (x - l / 2)/((x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBz3down(z, x, y, l, d):\n",
        "    factorcomun = (y + l / 2)/((y + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((x - l /2) ** 2 + (y + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBz4down(z, x, y, l, d):\n",
        "    factorcomun = (y - l / 2)/((y - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((x - l /2) ** 2 + (y - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y - l / 2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "## Este es la otra función que importa\n",
        "\n",
        "def SBzdown(z, x, y, l, d):\n",
        "    return SBz1down(z, x, y, l, d) - SBz2down(z, x, y, l, d) + SBz3down(z, x, y, l, d) - SBz4down(z, x, y, l, d)\n",
        "\n",
        "## Campo en la componente x\n",
        "\n",
        "def SBx1up(z, x, y, l, d):\n",
        "    factorcomun = (z + d/2)/((x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBx2up(z, x, y, l, d):\n",
        "    factorcomun = (z + d/2)/((x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBxup(z, x, y, l, d):\n",
        "    return SBx1up(z, x, y, l, d) - SBx2up(z, x, y, l, d)\n",
        "\n",
        "def SBx1down(z, x, y, l, d):\n",
        "    factorcomun = (z - d/2)/((x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBx2down(z, x, y, l, d):\n",
        "    factorcomun = (z - d/2)/((x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - y) / np.sqrt((y - l /2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + y) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBxdown(z, x, y, l, d):\n",
        "    return SBx1down(z, x, y, l, d) - SBx2down(z, x, y, l, d)\n",
        "\n",
        "## Campo en la componente y\n",
        "\n",
        "def SBy1up(z, x, y, l, d):\n",
        "    factorcomun = (z + d/2)/((y - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((y - l /2) ** 2 + (x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y - l / 2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBy2up(z, x, y, l, d):\n",
        "    factorcomun = (z + d/2)/((y + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((y + l /2) ** 2 + (x - l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z + d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SByup(z, x, y, l, d):\n",
        "    return SBy1up(z, x, y, l, d) - SBy2up(z, x, y, l, d)\n",
        "\n",
        "def SBy1down(z, x, y, l, d):\n",
        "    factorcomun = (z - d/2)/((y - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((y - l /2) ** 2 + (x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y - l / 2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBy2down(z, x, y, l, d):\n",
        "    factorcomun = (z - d/2)/((y + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    izquierda = (l / 2 - x) / np.sqrt((y + l /2) ** 2 + (x - l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    derecha = (l / 2 + x) / np.sqrt((y + l / 2) ** 2 + (x + l / 2) ** 2 + (z - d / 2) ** 2)\n",
        "    return C * factorcomun * (izquierda + derecha)\n",
        "\n",
        "def SBydown(z, x, y, l, d):\n",
        "    return SBy1down(z, x, y, l, d) - SBy2down(z, x, y, l, d)   "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dXaAiI1KsT9w"
      },
      "source": [
        "**Veamos la variacion de B y H a lo largo del borde de un Cubesat de 1U para BOBINAS CUADRADAS**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-PWnzKtEsNkF"
      },
      "source": [
        "l = 1   # longitud de la bobina [metros]\n",
        "d = 0.5445*l  # distancia de separación ideal\n",
        "\n",
        "dimensionx = 1  # tamaño del cubesat en x (en unidades U / 1U = 10cm)\n",
        "dimensiony = 1  # tamaño del cubesat en y\n",
        "dimensionz = 1  # tamaño del cubesat en z\n",
        "z = np.linspace(-d/2, d/2, 100) ## vamos a ver puntos desde una bobina hasta la otra\n",
        "y = dimensiony/20 #veamos los bordes de un Cubesat de 1U\n",
        "x = dimensionx/20\n",
        "Bzsquare = np.zeros(len(z))  # inicializamos los campos en x,y,z\n",
        "Bxsquare = np.zeros(len(z))\n",
        "Bysquare = np.zeros(len(z))\n",
        "\n",
        "Hsquare = np.zeros(len(z)) #inicializamos la homogeneidad\n",
        "#Campos en el centro\n",
        "Bzsquare0 = (SBzdown(0, 0, 0, l, d) + SBzup(0, 0, 0, l, d) )*(10 ** 6) \n",
        "Bxsquare0 = (SBxdown(0, 0, 0, l, d) + SBxup(0, 0, 0, l, d) )*(10 ** 6)\n",
        "Bysquare0 = (SBydown(0, 0, 0, l, d) + SByup(0, 0, 0, l, d) )*(10 ** 6)\n",
        "\n",
        "\n",
        "## En cada iteración calculamos los campos y la homogeneidad\n",
        "for i in range(len(z)):\n",
        "  Bzsquare[i] = (SBzdown(z[i], x, y, l, d) + SBzup(z[i], x, y, l, d) )*(10 ** 6)\n",
        "  Bxsquare[i] = (SBxdown(z[i], x, y, l, d) + SBxup(z[i], x, y, l, d) )*(10 ** 6) \n",
        "  Bysquare[i] = (SBydown(z[i], x, y, l, d) + SByup(z[i], x, y, l, d) )*(10 ** 6) \n",
        "  Hsquare[i] = (10 ** 6) * np.sqrt((Bzsquare[i] - Bzsquare0) ** 2)/np.abs(Bzsquare0)  #no consideramos campos no axiales"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SgIhh01Qt2Pc"
      },
      "source": [
        "**Veamos la variacion de H a lo largo del borde de un Cubesat de 1U para BOBINAS CIRCULARES**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g1Sv5rtKt7kl"
      },
      "source": [
        "r = 0.5 #radio de las bobinas [metro]\n",
        "d = r #distancia de separación ideal\n",
        "dimensionx = 1  # tamaño del cubesat en x (en unidades U / 1U = 10cm)\n",
        "dimensiony = 1  # tamaño del cubesat en y\n",
        "dimensionz = 1  # tamaño del cubesat en z\n",
        "z = np.linspace(-r/2, r/2, 100) ## vamos a ver puntos desde una bobina hasta la otra\n",
        "y = dimensiony/20 #veamos los bordes de un Cubesat de 1U\n",
        "x = dimensionx/20\n",
        "BzCirc = np.zeros(len(z))  # inicializamos los campos\n",
        "BxCirc = np.zeros(len(z))\n",
        "ByCirc = np.zeros(len(z))\n",
        "HCirc = np.zeros(len(z)) #inicializamos la homogeneidad\n",
        "\n",
        "## integral numérica en cuadraturas para los campos en el centro\n",
        "Lz0 = quad(dBzup, 0, 2*np.pi, args=(0, 0, 0, r, d)) + quad(dBzdown, 0, 2*np.pi, args=(0, 0, 0, r, d)) \n",
        "Ly0 = quad(dByup, 0, 2*np.pi, args=(0, 0, 0, r, d)) + quad(dBydown, 0, 2*np.pi, args=(0, 0, 0, r, d)) \n",
        "Lx0 = quad(dBxup, 0, 2*np.pi, args=(0, 0, 0, r, d)) + quad(dBxdown, 0, 2*np.pi, args=(0, 0, 0, r, d)) \n",
        "#campos en el centro\n",
        "BzCirc0 = (Lz0[0] + Lz0[2]) * 10 **6 \n",
        "ByCirc0 = (Ly0[0] + Ly0[2]) * 10 **6\n",
        "BxCirc0 = (Lx0[0] + Lx0[2]) * 10 **6\n",
        "\n",
        "## En cada iteración calculamos los campos y la homogeneidad\n",
        "for i in range(len(z)):\n",
        "## integral numérica en cuadraturas para los campos \n",
        "  Lz = quad(dBzup, 0, 2*np.pi, args=(z[i], x, y, r, d)) + quad(dBzdown, 0, 2*np.pi, args=(z[i],x, y, r, d))  \n",
        "  Lx = quad(dBxup, 0, 2*np.pi, args=(z[i], x, y, r, d)) + quad(dBxdown, 0, 2*np.pi, args=(z[i],x, y, r, d))   \n",
        "  Ly = quad(dByup, 0, 2*np.pi, args=(z[i], x, y, r, d)) + quad(dBydown, 0, 2*np.pi, args=(z[i],x, y, r, d))  \n",
        "  BzCirc[i] = (Lz[0] + Lz[2]) * 10 **6 \n",
        "  BxCirc[i] = (Lx[0] + Lx[2]) * 10 **6\n",
        "  ByCirc[i] = (Ly[0] + Ly[2]) * 10 **6    \n",
        "## homogeneidad sobre un borde\n",
        "  HCirc[i] = (10 ** 6) * np.sqrt((BzCirc[i] - BzCirc0) ** 2)/np.abs(BzCirc0) #no consideramos campos no axiales\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EvGV4a7q1PgZ"
      },
      "source": [
        "**Veamos la variación de H con el lado L de las BOBINAS CUADRADAS**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5FkL191J1Ow8"
      },
      "source": [
        "L = np.linspace(0.5,1.5,20)   # array de longitud de bobinas [metros]\n",
        "\n",
        "dimensionx = 1  # tamaño del cubesat en x (en unidades U / 1U = 10cm)\n",
        "dimensiony = 1  # tamaño del cubesat en y\n",
        "dimensionz = 1  # tamaño del cubesat en z\n",
        "z = dimensionz/20 ## vamos a ver puntos en un vertice del cubesat\n",
        "y = dimensiony/20 \n",
        "x = dimensionx/20\n",
        "\n",
        "HsquareL = np.zeros(len(L)) #inicializamos la homogeneidad\n",
        "\n",
        "## En cada iteración calculamos el campo y la homogeneidad\n",
        "for h in range(len(L)):\n",
        "  d = 0.5445*L[h]  # distancia de separación ideal\n",
        "  BzsquareL = (SBzdown(x, y, z, L[h], d) + SBzup(x, y, z, L[h], d) )*(10 ** 6) #Campo en el vértice\n",
        "  BzsquareL0 = (SBzdown(0, 0, 0, L[h], d) + SBzup(0, 0, 0, L[h], d) )*(10 ** 6) #Campo en el centro\n",
        "  HsquareL[h] = (10 ** 6) * np.sqrt((BzsquareL - BzsquareL0) ** 2)/np.abs(BzsquareL0)  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T5zZduTI4BHg"
      },
      "source": [
        "**Veamos la varación de H con el radio de las BOBINAS CIRCULARES**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fn4QtfVF3_5O"
      },
      "source": [
        "R = np.linspace(0.5/2,1.5/2,20)   # array de RADIOS de bobinas [metros]\n",
        "\n",
        "dimensionx = 1  # tamaño del cubesat en x (en unidades U / 1U = 10cm)\n",
        "dimensiony = 1  # tamaño del cubesat en y\n",
        "dimensionz = 1  # tamaño del cubesat en z\n",
        "z = dimensionz/20 ## vamos a ver puntos en un vertice del cubesat\n",
        "y = dimensiony/20 \n",
        "x = dimensionx/20\n",
        "\n",
        "HCircL = np.zeros(len(R)) #inicializamos la homogeneidad\n",
        "\n",
        "## En cada iteración calculamos el campo y la homogeneidad\n",
        "for h in range(len(R)):\n",
        "  d = R[h] #distancia de separación ideal\n",
        "## integral numérica en cuadraturas para los campos en z\n",
        "  Lz = quad(dBzup, 0, 2*np.pi, args=(z, x, y, R[h], d)) + quad(dBzdown, 0, 2*np.pi, args=(z,x, y, R[h], d))   \n",
        "  BzCircL = (Lz[0] + Lz[2]) * 10 **6   \n",
        "## campo en el centro\n",
        "  Lz0 = quad(dBzup, 0, 2*np.pi, args=(0, x, y, R[h], d)) + quad(dBzdown, 0, 2*np.pi, args=(0, x, y, R[h], d)) \n",
        "  BzCircL0 = (Lz0[0] + Lz0[2]) * 10 **6\n",
        "## homogeneidad sobre un borde\n",
        "  HCircL[h] = (10 ** 6) * np.sqrt((BzCircL - BzCircL0) ** 2)/np.abs(BzCircL0) "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W-fEWJx-5eSc"
      },
      "source": [
        "**GRAFICOS H VS Z + AJUSTES**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "2_rRK-Cc5jZh",
        "outputId": "4540e0e0-7c43-407f-aa06-c6be91aef3cc"
      },
      "source": [
        "def cuarta(x, a ,b):\n",
        "  return a * x ** (4) + b \n",
        "\n",
        "popt1, pvar1 =curve_fit(cuarta, z, HCirc) #ajuste cuártico para las bobinas circulares\n",
        "popt2, pvar2 =curve_fit(cuarta, z, Hsquare) ##ajuste cuártico para las bobinas cuadradas\n",
        "\n",
        "plt.plot(z, HCirc, 'b.')\n",
        "plt.plot(z, Hsquare, 'r.')\n",
        "plt.plot(z, cuarta(z, *popt1))\n",
        "plt.plot(z, cuarta(z, *popt2))\n",
        "plt.xlabel('z [m]')\n",
        "plt.ylabel('H [ppm]')\n",
        "plt.legend(['Bobinas circulares','Bobinas cuadradas', 'Ajuste z^4', 'Ajuste z^4'])\n",
        "plt.title('Homogneidad sobre el borde de un Cubesat de 1U')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pZzmGCM16zJ6"
      },
      "source": [
        "GRAFICOS H VS L + AJUSTES"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "-cad8ISU6yKd",
        "outputId": "acab0c63-6819-4e75-8aa2-a63610055c2c"
      },
      "source": [
        "def cuartaL(x, a ,b):\n",
        "  return a * x ** (-4) + b\n",
        "\n",
        "popt1, pvar1 =curve_fit(cuartaL, L, HCircL) #ajuste cuártico para las bobinas circulares\n",
        "popt2, pvar2 =curve_fit(cuartaL, L, HsquareL) ##ajuste cuártico para las bobinas cuadradas\n",
        "\n",
        "plt.plot(L, HCircL, 'b.')\n",
        "plt.plot(L, HsquareL, 'r.')\n",
        "plt.plot(L, cuartaL(L, *popt1))\n",
        "plt.plot(L, cuartaL(L, *popt2))\n",
        "plt.xlabel('L = 2 x R [m]')\n",
        "plt.ylabel('H [ppm]')\n",
        "plt.legend(['Bobinas circulares','Bobinas cuadradas', 'Ajuste L^(-4)', 'Ajuste L^(-4)'])\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Aoud3dZ8p-a"
      },
      "source": [
        "**MOSTREMOS POR QUÉ NO CONSIDERAMOS CAMPOS NO AXIALES EN ESTOS CÓDIGOS: GRÁFICOS B vs Z**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "PnRk0KeY8m36",
        "outputId": "04093af1-326d-4ca3-8bad-194e4d579bb7"
      },
      "source": [
        "plt.figure(1)\n",
        "plt.plot(z, BxCirc, 'blue')\n",
        "plt.plot(z, Bxsquare, 'red')\n",
        "plt.xlabel('z [m]')\n",
        "plt.ylabel('Bx [uT]')\n",
        "plt.legend(['Bobinas circulares', 'Bobinas cuadradas'])\n",
        "plt.title('Campo en x sobre el eje axial')\n",
        "plt.grid()\n",
        "\n",
        "plt.figure(2)\n",
        "plt.plot(z, BzCirc, 'blue')\n",
        "plt.plot(z, Bzsquare, 'red')\n",
        "plt.xlabel('z [m]')\n",
        "plt.ylabel('Bz [uT]')\n",
        "plt.legend(['Bobinas circulares', 'Bobinas cuadradas'])\n",
        "plt.title('Campo en z sobre el eje axial')\n",
        "plt.grid()\n",
        "\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}