pletchm/Phys326(Lab 1).ipynb

## Phys326(Lab 1).ipynb
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 "metadata": {
  "name": ""
 },
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 "worksheets": [
  {
   "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$$g$\n",
      "\n",
      "$r$ = $R-\\frac{D}{2}$\n",
      "\n",
      "$B$ = $\\alpha$$I$\n",
      "\n",
      "$\\alpha$ = $1.36 \\pm 0.03$ mT/A\n",
      "\n",
      "gravity: $g$ = $9.8\\frac{m}{s^2}$"
     ]
    },
    {
     "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",
      "\n",
      "$\\delta r$ = $\\sqrt{(\\delta D)^2+(\\delta R)^2}$\n",
      "\n",
      "$\\delta B$ = $\\sqrt{(\\frac{\\delta I}{I})^2+(\\frac{\\delta \\alpha}{\\alpha})^2}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Tabe of Data**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "|$m$$\\pm$$\\delta$$m$(kg)|$D$$\\pm$$\\delta$$D$(m)|$R$$\\pm$$\\delta$$R$(m)|$r$$\\pm$$\\delta$$r$(m)|$I$$\\pm$$\\delta$$I$(A)|$B$$\\pm$$\\delta$$B$(mT)|\n",
      "|-----------------------|----------------------|----------------------|-----------------------|----------------------|-----------------------|\n",
      "|$0.0012 \\pm 0.0001$     |$0.054 \\pm 0.001$     |$0.090 \\pm 0.005$     |$0.063 \\pm 0.005$      |$2.2 \\pm 0.1$         |$3.06 \\pm 0.15$        |\n",
      "|$0.0012 \\pm 0.0001$     |$0.054 \\pm 0.001$     |$0.093 \\pm 0.005$     | $0.064 \\pm 0.005$     |$2.3 \\pm 0.1$         |$3.33 \\pm 0.16$        |\n",
      "|$0.0012 \\pm 0.0001$     |$0.054 \\pm 0.001$     |$0.093 \\pm 0.005$     |$0.064 \\pm 0.005$      |$2.4 \\pm 0.1$         |$3.67 \\pm 0.17$        |"
     ]
    },
    {
     "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": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B=np.array([3.06,3.33,3.67])\n",
      "dB=np.array([0.15,0.16,0.17])\n",
      "r=np.array([0.063,0.064,0.064])\n",
      "dr=np.array([0.005,0.005,0.005])\n",
      "\n",
      "\n",
      "fig,ax=plt.subplots(1,1,)\n",
      "plt.errorbar(B,r,xerr=dB, fmt='ko')\n",
      "plt.errorbar(B,r,yerr=dr,fmt='ko')\n",
      "ax.plot(B,r,'ro',label=\"measurement\")\n",
      "ax.plot([0,4],[0.063,0.064],'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": [
        "[ 440.    -24.66]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FEovi62tyShcAcHR0xNdff43169cDqB6Et3PnTgwePLjZFXYkBgYGcpvLi3Qe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\nb4dOp8POzg4yMzP9HtddXl7OzPfl5ORArVZjb28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       "text": [
        "<matplotlib.figure.Figure at 0x7f8e6a7aa690>"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given the relationship between $\\mu$ and the slope, Let slope = $S$\n",
      "\n",
      "   $S$ = $\\frac{\\mu}{mg}$\n",
      "\n",
      "we can solve for $\\mu$ and its uncertainty. My best estimation for the slope of the line\n",
      "\n",
      "$S$ = $\\frac{r1-r3}{B1-B3}$\n",
      "\n",
      "$S$ = $\\frac{(.064m-.063m)}{(3.67mT-3.06mT)}$\n",
      "\n",
      "$S$ = $0.0016$\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",
      "\n",
      "$\\delta$$S$ = $\\sqrt{(\\frac{\\delta r}{r})^2+(\\frac{\\delta B}{B})^2}$\n",
      "\n",
      "$\\delta$$S$ = $ .0001$\n",
      "\n",
      "So we now we multiply $S$$\\pm$$\\delta$$S$ by $mg$ which my mass $m$ uncertainty so we must the quadratic sum again. This gives us the a value for $\\mu$ of\n",
      "\n",
      "$\\delta \\mu$ = $\\sqrt{(\\frac{\\delta S}{S})^2+(\\frac{\\delta m}{m})^2}$\n",
      "\n",
      "$\\delta \\mu$ = $0.142 $\n",
      "\n",
      "$\\mu$ = $1.36 \\pm 0.142$\n",
      "\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}