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+{

+ "metadata": {

+  "name": "",

+  "signature": "sha256:1ba9d8e44f464fdd4be85263413cd33050741f89efba47984e88555948ca8361"

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "7: Magnetic Properties"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.1, Page number 7.3"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "M = 1.4      #field(T)\n",

+      "H = 6.5*10**-4      #magnetic field(T)\n",

+      "\n",

+      "#Calculation\n",

+      "chi = M/H      #susceptibility\n",

+      "mew_r = 1+chi       #relative permeability\n",

+      "\n",

+      "#Result\n",

+      "print \"relative permeability of iron is\",round(mew_r)\n",

+      "print \"answer given in the book is wrong\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "relative permeability of iron is 2155.0\n",

+        "answer given in the book is wrong\n"

+       ]

+      }

+     ],

+     "prompt_number": 2

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.2, Page number 7.3"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "M = 3300     #magnetisation(amp/m)\n",

+      "H = 220      #field strength(amp/m)\n",

+      "\n",

+      "#Calculation\n",

+      "mew_r = (M/H)+1      #relative permeability\n",

+      "\n",

+      "#Result\n",

+      "print \"relative permeability of material is\",mew_r"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "relative permeability of material is 16.0\n"

+       ]

+      }

+     ],

+     "prompt_number": 3

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.3, Page number 7.4"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "H = 10**6      #magnetic field intensity(amp/m)\n",

+      "chi = 1.5*10**-3     #susceptibility\n",

+      "\n",

+      "#Calculation\n",

+      "mew0 = 4*math.pi*10**-7\n",

+      "M = chi*H      #magnetisation(A/m)\n",

+      "B = mew0*(M+H)      #flux density(T)\n",

+      "M = M*10**-3\n",

+      "B = math.ceil(B*10**3)/10**3   #rounding off to 3 decimals\n",

+      "\n",

+      "#Result\n",

+      "print \"magnetisation of material is\",M,\"*10**3 A/m\"\n",

+      "print \"flux density is\",B,\"T\"\n",

+      "print \"answer for flux density B given in the book is wrong\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "magnetisation of material is 1.5 *10**3 A/m\n",

+        "flux density is 1.259 T\n",

+        "answer for flux density B given in the book is wrong\n"

+       ]

+      }

+     ],

+     "prompt_number": 5

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.4, Page number 7.5"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "H = 10**4      #magnetic field intensity(amp/m)\n",

+      "chi = 3.7*10**-3     #susceptibility\n",

+      "\n",

+      "#Calculation\n",

+      "mew0 = 4*math.pi*10**-7\n",

+      "M = chi*H      #magnetisation(A/m)\n",

+      "B = mew0*(M+H)      #flux density(Wb/m**2)\n",

+      "B = math.ceil(B*10**5)/10**5   #rounding off to 5 decimals\n",

+      "\n",

+      "#Result\n",

+      "print \"magnetisation of material is\",M,\"A/m\"\n",

+      "print \"flux density is\",B,\"Wb/m**2\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "magnetisation of material is 37.0 A/m\n",

+        "flux density is 0.01262 Wb/m**2\n"

+       ]

+      }

+     ],

+     "prompt_number": 6

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.5, Page number 7.14"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "I = 500     #current(mA)\n",

+      "d = 10     #diameter(cm)\n",

+      "\n",

+      "#Calculation\n",

+      "I = I*10**-3     #current(A)\n",

+      "r = d/2    #radius(cm)\n",

+      "r = r*10**-2    #radius(m)\n",

+      "A = 2*math.pi*r**2   #area(m**2)\n",

+      "mew_m = I*A     #magnetic moment(Am**2)\n",

+      "mew_m = mew_m*10**3\n",

+      "mew_m = math.ceil(mew_m*10**3)/10**3   #rounding off to 3 decimals\n",

+      "\n",

+      "#Result\n",

+      "print \"magnetic moment associated with the loop is\",mew_m,\"*10**-3 Am**2\"\n",

+      "print \"answer given in the book is wrong in the 3rd decimal\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "magnetic moment associated with the loop is 7.854 *10**-3 Am**2\n",

+        "answer given in the book is wrong in the 3rd decimal\n"

+       ]

+      }

+     ],

+     "prompt_number": 9

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.6, Page number 7.19"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "r = 5.29*10**-11    #radius of orbit(m)\n",

+      "B = 2     #field applied(T)\n",

+      "e = 1.602*10**-19     #charge of electron(coulomb)\n",

+      "m = 9.108*10**-31    #mass of electron(kg)\n",

+      "\n",

+      "#Calculation\n",

+      "mew_ind = e**2*r**2*B/(4*m)      #change in magnetic moment(Am^2)\n",

+      "\n",

+      "#Result\n",

+      "print \"change in magnetic moment is\",round(mew_ind/1e-29,3),\"*10^-29 Am**2\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "change in magnetic moment is 3.943 *10^-29 Am**2\n"

+       ]

+      }

+     ],

+     "prompt_number": 12

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.7, Page number 7.22"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "chi_1 = 2.8*10**-4     #susceptibility\n",

+      "T1 = 350      #temperature(K)\n",

+      "T2 = 300      #temperature(K)\n",

+      "\n",

+      "#Calculation\n",

+      "#chi = C/T where C is curie constant\n",

+      "chi_2 = chi_1*T1/T2     #susceptibility at 300 K\n",

+      "chi_2 = chi_2*10**4\n",

+      "chi_2 = math.ceil(chi_2*10**3)/10**3   #rounding off to 3 decimals\n",

+      "\n",

+      "#Result\n",

+      "print \"susceptibility at 300 K is\",chi_2,\"*10**-4\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "susceptibility at 300 K is 3.267 *10**-4\n"

+       ]

+      }

+     ],

+     "prompt_number": 13

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.8, Page number 7.28"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "d = 8906     #density(kg/m**3)\n",

+      "n = 6.025*10**26     #avagadro number\n",

+      "AW = 58.7     #atomic weight\n",

+      "Bs = 0.65     #magnetic induction(Wb/m**2)\n",

+      "mewB = 9.27*10**-24 \n",

+      "\n",

+      "#Calculation\n",

+      "N = d*n/AW     #number of atoms(per m**3)\n",

+      "mew0 = 4*math.pi*10**-7\n",

+      "mew_m = Bs/(N*mew0)      #magnetic moment(Am**2)\n",

+      "mew_m = mew_m/mewB       #magnetic moment(mewB)\n",

+      "mew_m = math.ceil(mew_m*10**3)/10**3   #rounding off to 3 decimals\n",

+      "\n",

+      "#Result\n",

+      "print \"the magnetic moment of Ni is\",mew_m,\"mewB\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "the magnetic moment of Ni is 0.611 mewB\n"

+       ]

+      }

+     ],

+     "prompt_number": 14

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.9, Page number 7.29"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "H = 2     #magnetic field(Wb/m**2)\n",

+      "mew = 9.4*10**-24\n",

+      "k = 1.38*10**-23\n",

+      "\n",

+      "#Calculation\n",

+      "#np = C*n0*math.exp(mew*H/(k*T))\n",

+      "#na = C*n0*math.exp(-mew*H/(k*T))\n",

+      "#np/na = exp(mew*H/(k*T))/exp(-mew*H/(k*T)) = exp(2*mew*H/(k*T))\n",

+      "#given np/na = 2. therefore exp(2*mew*H/(k*T)) = 2\n",

+      "T = 2*mew*H/(k*math.log(2))    #temperature(K)\n",

+      "T = math.ceil(T*10**2)/10**2   #rounding off to 2 decimals\n",

+      "\n",

+      "#Result\n",

+      "print \"temperature is\",T,\"K\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "temperature is 3.94 K\n"

+       ]

+      }

+     ],

+     "prompt_number": 15

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example number 7.10, Page number 7.30"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#importing modules\n",

+      "import math\n",

+      "from __future__ import division\n",

+      "\n",

+      "#Variable declaration\n",

+      "AW = 157.26      #atomic weight\n",

+      "d = 7.8*10**3     #density(kg/m**3)\n",

+      "A = 6.025*10**26     #avagadro number\n",

+      "mew0 = 4*math.pi*10**-7\n",

+      "N = d*A/AW      #number of atoms 1 kg contains\n",

+      "g = N/10**3      #number of atoms 1 g contains\n",

+      "mew_B = 7.1      #bohr magneton\n",

+      "mew_m = 9.27*10**-24\n",

+      "mew_mg = g*mew_B*mew_m     #magnetic moment per gram(Am**2)\n",

+      "mew_mg = math.ceil(mew_mg*10**3)/10**3   #rounding off to 3 decimals\n",

+      "print \"magnetic moment per gram is\",mew_mg,\"Am**2\"\n",

+      "Bs = N*mew0*mew_m      #saturation magnetisation(Wb/m**2)\n",

+      "Bs = math.ceil(Bs*10**4)/10**4   #rounding off to 4 decimals\n",

+      "print \"saturation magnetisation is\",Bs,\"Wb/m**2\"\n",

+      "print \"answers given in the book are wrong\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "magnetic moment per gram is 1966.852 Am**2\n",

+        "saturation magnetisation is 0.3482 Wb/m**2\n",

+        "answers given in the book are wrong\n"

+       ]

+      }

+     ],

+     "prompt_number": 16

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
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