SNOWs_Inductance.ipynb

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      "name": "SNOWs_Inductance.ipynb",
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        "<a href=\"https://colab.research.google.com/github/osnove/Dodatno/blob/master/SNOWs_Inductance.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# SNOWs formula for inductance of a single layer solenoid\n",
        "\n",
        "\n",
        "This is quite accurate formula for a single layer solenoid. Formula comes from the paper\n",
        "http://www.coe.ufrj.br/~acmq/tesla/maxwell.pdf\n",
        " and compares well with Kirchoffs and Maxwells formulas. "
      ]
    },
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        "id": "IIJIE7k9ph2_",
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      },
      "source": [
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib\n",
        "import scipy.special as special"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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      "source": [
        "a=0.486 #5e-2  # coil raduis\n",
        "b=0.0921  #4e-2  # coil height\n",
        "c=0.0095  #1.88e-3  # coil diameter\n",
        "n=5   # number of coils\n",
        "pi=np.pi\n",
        "mi_0=4*pi*1e-7"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
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      "source": [
        "p=2*a/b\n",
        "theta=np.arctan(p)\n",
        "k=np.sin(theta)\n",
        "k1=np.cos(theta)\n",
        "z=pi*n*c/b"
      ],
      "execution_count": 0,
      "outputs": []
    },
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        }
      },
      "source": [
        "K=special.ellipk(k) # elliptic integral of a first  kind\n",
        "E=special.ellipe(k) # elliptic integral of a second  kind\n",
        "\n",
        "\n",
        "%whos\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
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          "text": [
            "Variable     Type       Data/Info\n",
            "---------------------------------\n",
            "E            float64    1.008021304684566\n",
            "K            float64    4.0961576922801575\n",
            "L            float64    1.98269910975166e-05\n",
            "S1           float64    199.84660832730418\n",
            "S2           float64    -0.6290450162020763\n",
            "S3           float64    0.10305798056070045\n",
            "S4           float64    0.31999368858514404\n",
            "a            float      0.486\n",
            "b            float      0.0921\n",
            "c            float      0.0095\n",
            "k            float64    0.9955409295862284\n",
            "k1           float64    0.09433057573548517\n",
            "math         module     <module 'math' (built-in)>\n",
            "matplotlib   module     <module 'matplotlib' from<...>/matplotlib/__init__.py'>\n",
            "mi_0         float      1.2566370614359173e-06\n",
            "n            int        5\n",
            "np           module     <module 'numpy' from '/us<...>kages/numpy/__init__.py'>\n",
            "p            float      10.553745928338762\n",
            "pi           float      3.141592653589793\n",
            "plt          module     <module 'matplotlib.pyplo<...>es/matplotlib/pyplot.py'>\n",
            "special      module     <module 'scipy.special' f<...>ipy/special/__init__.py'>\n",
            "theta        float64    1.4763252916068947\n",
            "z            float      1.6202567974540192\n"
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        ""
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      "source": [
        "S1=8*n**2*a*pi/3*((K+(p**2-1)*E)/k-p*p)\n",
        "S2=2*n*(1/4-np.log(z))+1/3*np.log(2*pi*n*a/b)-4/pi**2*(E/k-1)*(1+z**2/8)\n",
        "S3=-2/3*((K-E)/k-k*K/2)-k1/(2*k)*(1-k1*theta/k)\n",
        "S4=np.log((1+k1)/(1-k1))+k1*np.log(4)\n"
      ],
      "execution_count": 0,
      "outputs": []
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      "cell_type": "code",
      "metadata": {
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      },
      "source": [
        "L=mi_0/(4*pi)*(S1+2*pi*a*(S2+S3)+b*S4)"
      ],
      "execution_count": 0,
      "outputs": []
    },
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        "%whos"
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      "outputs": [
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          "text": [
            "Variable     Type       Data/Info\n",
            "---------------------------------\n",
            "E            float64    1.008021304684566\n",
            "K            float64    4.0961576922801575\n",
            "L            float64    4.5368905947438836e-05\n",
            "S1           float64    457.86893963105894\n",
            "S2           float64    -0.6290450162020763\n",
            "S3           float64    -0.7494305196721343\n",
            "S4           float64    0.31999368858514404\n",
            "a            float      0.486\n",
            "b            float      0.0921\n",
            "c            float      0.0095\n",
            "k            float64    0.9955409295862284\n",
            "k1           float64    0.09433057573548517\n",
            "math         module     <module 'math' (built-in)>\n",
            "matplotlib   module     <module 'matplotlib' from<...>/matplotlib/__init__.py'>\n",
            "mi_0         float      1.2566370614359173e-06\n",
            "n            int        5\n",
            "np           module     <module 'numpy' from '/us<...>kages/numpy/__init__.py'>\n",
            "p            float      10.553745928338762\n",
            "pi           float      3.141592653589793\n",
            "plt          module     <module 'matplotlib.pyplo<...>es/matplotlib/pyplot.py'>\n",
            "special      module     <module 'scipy.special' f<...>ipy/special/__init__.py'>\n",
            "theta        float64    1.4763252916068947\n",
            "z            float      1.6202567974540192\n"
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          "name": "stdout"
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "4**2/2"
      ],
      "execution_count": 0,
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          "output_type": "execute_result",
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            "text/plain": [
              "8.0"
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