Phys326(Lab 1).ipynb

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  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Magnetic Moment Experiment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Magnetic Moment Experiment: This is my first experiment with IPython notebook. Here is where I will take my notes."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Variables**\n",
      "\n",
      "mass of the weight: $m$\n",
      "\n",
      "Diameter of the ball: $D$\n",
      "\n",
      "Midway between coils: $\\alpha$\n",
      "\n",
      "Magnetic Field: $B$\n",
      "\n",
      "Current: $I$\n",
      "\n",
      "Distance from farside of ball to center of mass of the weight: $R$\n",
      "\n",
      "Distance from center of ball to center of mass of the weight: $r$\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Equations and Given Values**\n",
      "\n",
      "Magnetic Torque: $\\tau$ = $\\mu$ $\\times$ $B$\n",
      "\n",
      "Gravitational Torque: $\\tau$ = $r$ $\\times$ $m$$g$\n",
      "\n",
      "$r$ = $R$ - $D$$/$$2$\n",
      "\n",
      "$B$ = $\\alpha$$I$\n",
      "\n",
      "$\\alpha$ = $1.36 \\pm 0.03$ mT/A\n",
      "\n",
      "gravity: g = $9.8$ m/s$^2$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Strategies**\n",
      "\n",
      "I measured the diameter of the ball to 54mm but I predicted that my accuracy could have been distorted up to a whole milimeter so I decided that my error should be 1mm. I measured the distance from the center of the ball to the center of the mass to be 90mm and, similarly to my error in the diameter of the ball, I thought I realistically could have been off by a half of a milimeter. So then when it came to subtracting them I added their uncertainties by the rule of sums. Later when calculating the magnetic field we had to multiply our measure current and by our given value for $\\alpha$. In this calculation I had to use the quadratic error propigation method.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Tabe of Data**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "|$m$$\\pm$$\\delta$$m$(kg)|$D$$\\pm$$\\delta$$D$(m)|$I$$\\pm$$\\delta$$I$(A)|$R$$\\pm$$\\delta$$R$(m)|$r$$\\pm$$\\delta$$r$(m)|$B$$\\pm$$\\delta$$B$(mT)|\n",
      "|-----------------------|----------------------|----------------------|--------------------|-------------------|---------------------------|\n",
      "|$0.0012 \\pm 0.001$     |$0.054 \\pm 0.001$     |$2.2 \\pm 0.1$         |$0.090 \\pm 0.005$   |$0.063 \\pm 0.006$  |$3.06 \\pm 0.10$            |\n",
      "|$0.0012 \\pm 0.001$     |$0.054 \\pm 0.001$     |$2.3 \\pm 0.1$         |$0.093 \\pm 0.005$   |$0.064 \\pm 0.006$  |$3.33 \\pm 0.28$            |\n",
      "|$0.0012 \\pm 0.001$     |$0.054 \\pm 0.001$     |$2.4 \\pm 0.1$         |$0.081 \\pm 0.01$   |$0.055 \\pm 0.011$  |$3.67 \\pm 0.11$             |"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B=np.array([3.06,3.33,3.67])\n",
      "dB=np.array([0.1,0.28,0.11])\n",
      "r=np.array([0.063,0.064,0.055])\n",
      "dr=np.array([0.006,0.006,0.011])\n",
      "\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([0,4],[0.05,0.06],'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",
      "print(regression)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-52.53424658   6.54041096]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZlZUVmzhxIsvPz2eMMZaSksIEAgHbtWsXc3BwYJaWlmzLli0sLi6OderUiVlYWLC5c+fK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\nn/q6deuGjIwMmJqaIioqCqNHj8aDBw8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       "text": [
        "<matplotlib.figure.Figure at 0x7fbb39dd2d90>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given the relationship between $\\mu$ and the slope, Let slope = $S$\n",
      "\n",
      "   $S$ = $\\mu$$/$$m$$g$\n",
      "\n",
      "we can solve for $\\mu$ and its uncertainty. My best estimation for the slope of the line\n",
      "\n",
      "$S$$ = $$(.064-.063)$$/$$(3.33-3.06)$\n",
      "\n",
      "$ = $$0.0037$\n",
      "\n",
      "So then our error of the line is sum of the points we used then since we took the ratio of those distance we take the quadratic sum of the two error values. So we get \n",
      "\n",
      "$\\delta$$S$ $=$ 0.38\n",
      "\n",
      "So we now we multiply $S$$\\pm$$\\delta$$S$ by $m$$g$ which my mass $m$ uncertainty so we must the quadratic sum again. This gives us the a value for $\\mu$ of \n",
      "\n",
      "$\\mu$ $=$ $0.000044 \\pm 0.38$\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}