phys326Lab2.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np \n",
      "from matplotlib import pyplot as plt\n",
      "%matplotlib inline\n",
      "from pylab import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data=np.loadtxt(\"Magnetic+Moment+Measurements+Survey.csv\", delimiter=',')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(40, 4)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[0:3:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([[  1.32000000e+00,   5.00000000e-02,   5.36500000e+01,\n",
        "          5.00000000e-02],\n",
        "       [  1.48000000e+00,   3.00000000e-02,   5.36400000e+01,\n",
        "          1.00000000e-01],\n",
        "       [  1.20000000e+00,   1.00000000e-01,   5.36300000e+01,\n",
        "          5.00000000e-01]])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m=data[:,0]\n",
      "dm=data[:,1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([ 1.32,  1.48,  1.2 ,  1.4 ,  1.48,  1.8 ,  1.4 ,  1.3 ,  1.2 ,\n",
        "        1.4 ,  1.2 ,  1.2 ,  1.61,  1.61,  1.1 ,  1.6 ,  2.1 ,  1.4 ,\n",
        "        1.54,  1.4 ,  1.6 ,  1.4 ,  1.3 ,  1.55,  1.32,  1.6 ,  1.1 ,\n",
        "        1.1 ,  1.5 ,  1.2 ,  1.2 ,  1.5 ,  1.6 ,  1.4 ,  1.5 ,  1.4 ,\n",
        "        1.6 ,  1.4 ,  1.41,  1.4 ])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the mean mass."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z=sum(m)/40\n",
      "z"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "1.4205000000000001"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "My mass is 1.2 grams with an uncertainty of .1 grams, so I would change my .3 to include the mean."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dz=(sum((m-sum(m)/40)**2)/40)**.5\n",
      "dz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "0.19679875507736319"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the standard deviation of uncertainty in the mass measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q=dz/(40**.5)\n",
      "q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "0.031116615336504699"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the weighted mean of our mass measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W=(sum(1/((m-z)**2)*m))/sum(1/((m-z)**2))\n",
      "W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "1.4053558594046851"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of the weighted mean."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dW=1/((sum(1/((m-z)**2))**.5))\n",
      "dW"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "0.0053649383029114308"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.histogram(m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "(array([ 9,  0, 14,  3,  5,  7,  1,  0,  0,  1]),\n",
        " array([ 1.1,  1.2,  1.3,  1.4,  1.5,  1.6,  1.7,  1.8,  1.9,  2. ,  2.1]))"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the Histogram for measurements of mass. I plotted a Gaussian over it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "(hist,bins,m)=plt.hist(m,bins=20,normed=True)\n",
      "plt.plot(bins,(1/(dz*(2*np.pi)**.5)*np.exp((-(bins-z)**2/(2*dz**2)))))\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAW0AAAEACAYAAAB4ayemAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbRERgyi0RUQMotAWETGIQltExCD/B8aAwGWSjYdPAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb4b15f2b50>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m=data[:,0]\n",
      "dm=data[:,1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=np.array(m)\n",
      "y=np.array(dm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "array([ 1.32,  1.48,  1.2 ,  1.4 ,  1.48,  1.8 ,  1.4 ,  1.3 ,  1.2 ,\n",
        "        1.4 ,  1.2 ,  1.2 ,  1.61,  1.61,  1.1 ,  1.6 ,  2.1 ,  1.4 ,\n",
        "        1.54,  1.4 ,  1.6 ,  1.4 ,  1.3 ,  1.55,  1.32,  1.6 ,  1.1 ,\n",
        "        1.1 ,  1.5 ,  1.2 ,  1.2 ,  1.5 ,  1.6 ,  1.4 ,  1.5 ,  1.4 ,\n",
        "        1.6 ,  1.4 ,  1.41,  1.4 ])"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([ 0.05 ,  0.03 ,  0.1  ,  0.05 ,  0.05 ,  0.1  ,  0.05 ,  0.1  ,\n",
        "        0.05 ,  0.1  ,  0.1  ,  0.1  ,  0.02 ,  0.02 ,  0.1  ,  0.1  ,\n",
        "        1.5  ,  0.05 ,  0.005,  0.05 ,  0.05 ,  0.05 ,  0.1  ,  0.1  ,\n",
        "        0.01 ,  0.2  ,  0.1  ,  0.1  ,  0.05 ,  0.01 ,  0.1  ,  0.1  ,\n",
        "        0.05 ,  0.5  ,  0.1  ,  0.05 ,  0.05 ,  0.05 ,  0.05 ,  0.1  ])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data[2:3:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "array([[  1.2 ,   0.1 ,  53.63,   0.5 ]])"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c=data[:,2]\n",
      "dD=data[:,3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because one persons measurement of the diameter was so much of an outlier I omitted it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D=c[c>50]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the mean Diameter"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v=sum(D)/39\n",
      "v"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "53.656153846153863"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "My diameter is 54 milimeters with an uncertainty of 1 milimeter, so I would leave my error bars as they are on the graph from Lab 1."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dv=(sum((D-sum(D)/39)**2)/39)**.5\n",
      "dv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "0.12626011784012373"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the Standard deviation of mean for the diameter measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s=dv/(39**.5)\n",
      "s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "0.020217799568951759"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the weighted mean of the diameter measurements."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W=(sum(1/((D-v)**2)*D))/sum(1/((D-v)**2))\n",
      "W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "53.654310036534177"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of the weighted mean."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dW=1/((sum(1/((m-z)**2))**.5))\n",
      "dW"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "0.0053649383029114308"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the Histogram for the measurements of the diameter. I plotted the Gaussian over it.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(hist,bins,p)=plt.hist(D,bins=20,normed=True)\n",
      "plt.plot(bins,(1/(dv*(2*np.pi)**.5)*np.exp(-(bins-v)**2/(2*dv**2))))\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEACAYAAACnJV25AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb4b15f27d0>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x=np.array(c)\n",
      "y=np.array(dD)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "array([ 53.65,  53.64,  53.63,  53.64,  53.6 ,  53.64,  53.62,  53.6 ,\n",
        "        53.6 ,  53.34,  54.  ,  53.64,  53.64,  53.64,  53.66,  53.65,\n",
        "        53.6 ,  50.  ,  53.95,  53.6 ,  53.64,  53.62,  53.64,  53.55,\n",
        "        53.65,  54.  ,  53.66,  53.66,  53.65,  53.64,  54.  ,  53.61,\n",
        "        53.65,  53.62,  53.65,  53.64,  53.66,  53.62,  53.64,  53.45])"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$B$ = $\\alpha$$I$\n",
      "\n",
      "$\\alpha$ = $1.36 \\pm 0.03$ mT/A\n",
      "\n",
      "$r$ = $R-\\frac{D}{2}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I=np.array([2.2,2.3,2.4])\n",
      "dI=0.1\n",
      "alpha=1.36\n",
      "dalpha=.03\n",
      "R=np.array([0.090,0.093,0.093])\n",
      "dR=.005\n",
      "di=(sum(c)/40)/1000\n",
      "di\n",
      "ddi=np.sqrt((sum((c/1000)-di)**2)/40)\n",
      "ddi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 218,
       "text": [
        "1.0971354589302191e-17"
       ]
      }
     ],
     "prompt_number": 218
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B=I*alpha\n",
      "dB=B*np.sqrt((dI/I)**2+(dalpha/alpha)**2)\n",
      "\n",
      "r=R-(di)/2\n",
      "dr=dR+(ddi)/2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 219
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=(np.sum(B*B)*np.sum(r)-np.sum(B)*np.sum(B*r))/(3*np.sum(B*B)-(np.sum(B))**2) #y-intercept\n",
      "b=(3*np.sum(B*r)-np.sum(B)*np.sum(r))/(3*np.sum(B*B)-(np.sum(B))**2) #slope\n",
      "\n",
      "wa=(sum((B**2/(dr**2)))*sum(r/(dr**2))-sum(B/(dr**2))*sum((B*r)/(dr**2)))/(sum(1/(dr**2))*sum((B**2)/(dr**2))-(sum(B/(r**2)))**2)\n",
      "#y-intercept of weighted line.\n",
      "wb=(sum(1/(dr**2))*sum((B*r)/(dr**2))-sum(B/(dr**2))*sum(r/(dr**2)))/(sum(1/(dr**2))*sum((B**2)/(dr**2))-(sum(B/(dr**2)))**2)\n",
      "#slope of weighted line\n",
      "fig,ax=plt.subplots(1,1,)\n",
      "ax.errorbar(B,r,dB,dr,'ko') \n",
      "ax.plot(B,r,'ro',label=\"measurement\")\n",
      "ax.plot([2.9,3.4],[0.04,0.06],'k-',label=\"unity\")\n",
      "ax.legend(loc='best')\n",
      "ax.set_title('Magnetic Moment')\n",
      "ax.set_xlabel('Magnetic Field (mT)',fontsize=12)\n",
      "ax.set_ylabel('Distance from Center of the Ball to Weight (m)',fontsize=12)\n",
      "regression=np.polyfit(r,B,1)\n",
      "plt.plot(B,a+b*B)\n",
      "plt.plot(B,wa+wb*B)\n",
      "print(regression)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 68.         -1.3067985]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEpCAYAAABfpm8IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb4b09bec90>"
       ]
      }
     ],
     "prompt_number": 272
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "My weighted line is apparently completely overlapped with my best fit line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 225,
       "text": [
        "0.030717625000007107"
       ]
      }
     ],
     "prompt_number": 225
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When we make a polyfit of the line doesn't correlate to the data at all."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 226,
       "text": [
        "0.011029411764702115"
       ]
      }
     ],
     "prompt_number": 226
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.polyfit(B,r,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 227,
       "text": [
        "array([ 0.01102941,  0.03071762])"
       ]
      }
     ],
     "prompt_number": 227
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The values correlate to the ones that I calcuated"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the uncertainty of our line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S=(sum((r-b*B-a)**2)/40)**.5\n",
      "S"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 228,
       "text": [
        "0.00019364916731037102"
       ]
      }
     ],
     "prompt_number": 228
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty of the y-intercept."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "da=S*(sum(B**2)/(40*sum(B**2)-(sum(B))**2))**.5\n",
      "da"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 229,
       "text": [
        "3.1834102657501891e-05"
       ]
      }
     ],
     "prompt_number": 229
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty of the slope."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "db=S*(40/(40*sum(B**2)-(sum(B)**2)))**.5\n",
      "db"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 230,
       "text": [
        "3.7138276999790356e-05"
       ]
      }
     ],
     "prompt_number": 230
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M=(sum(m)/40)/1000\n",
      "M"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 231,
       "text": [
        "0.0014205000000000001"
       ]
      }
     ],
     "prompt_number": 231
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty in the mass is"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dM=np.sqrt(sum((M-(m/1000))**2)/40)\n",
      "dM"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 232,
       "text": [
        "0.0001967987550773633"
       ]
      }
     ],
     "prompt_number": 232
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty in the slope is"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "db=S*(40/(40*sum(B**2)-(sum(B)**2)))**.5\n",
      "db"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 233,
       "text": [
        "3.7138276999790356e-05"
       ]
      }
     ],
     "prompt_number": 233
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 234,
       "text": [
        "0.011029411764702115"
       ]
      }
     ],
     "prompt_number": 234
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is my best estimate for the magnetic moment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu=b*M*9.8\n",
      "mu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 235,
       "text": [
        "0.00015353933823524169"
       ]
      }
     ],
     "prompt_number": 235
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The uncertainty for the magnetic moment is "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dmu=mu*np.sqrt((db/b)**2+(dM/M)**2)\n",
      "dmu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 237,
       "text": [
        "2.1277911931858684e-05"
       ]
      }
     ],
     "prompt_number": 237
    }
   ],
   "metadata": {}
  }
 ]
}