path: root/ENGINEERING_PHYSICS_by_M.ARUMUGAM/Chapter06.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Chapter 6:Magnetic Properties and Crystal Structures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.1, Page number 6.46"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "temperature rise is 8.43 K\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "El=10**-2*50;      #energy loss(J)\n",
    "H=El*60;           #heat produced(J)\n",
    "d=7.7*10**3;       #iron rod(kg/m**3)\n",
    "s=0.462*10**-3;    #specific heat(J/kg K)\n",
    "\n",
    "#Calculation\n",
    "theta=H/(d*s);     #temperature rise(K)\n",
    "\n",
    "#Result\n",
    "print \"temperature rise is\",round(theta,2),\"K\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.2, Page number 6.46"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "magnetic field at the centre is 14.0 weber/m**2\n",
      "dipole moment is 9.0 *10**-24 ampere/m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "e=1.6*10**-19;    #charge(coulomb)\n",
    "new=6.8*10**15;   #frequency(revolutions per second)\n",
    "mew0=4*math.pi*10**-7;\n",
    "R=5.1*10**-11;     #radius(m)\n",
    "\n",
    "#Calculation\n",
    "i=round(e*new,4);          #current(ampere)\n",
    "B=mew0*i/(2*R);            #magnetic field at the centre(weber/m**2)\n",
    "A=math.pi*R**2;\n",
    "d=i*A;                    #dipole moment(ampere/m**2)\n",
    "\n",
    "#Result\n",
    "print \"magnetic field at the centre is\",round(B),\"weber/m**2\"\n",
    "print \"dipole moment is\",round(d*10**24),\"*10**-24 ampere/m**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.3, Page number 6.46"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intensity of magnetisation is 5.0 ampere/m\n",
      "flux density in material is 1.257 weber/m**2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "chi=0.5*10**-5;    #magnetic susceptibility\n",
    "H=10**6;     #field strength(ampere/m)\n",
    "mew0=4*math.pi*10**-7;\n",
    "\n",
    "#Calculation\n",
    "I=chi*H;     #intensity of magnetisation(ampere/m)\n",
    "B=mew0*(I+H);    #flux density in material(weber/m**2)\n",
    "\n",
    "#Result\n",
    "print \"intensity of magnetisation is\",I,\"ampere/m\"\n",
    "print \"flux density in material is\",round(B,3),\"weber/m**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.4, Page number 6.47"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of Bohr magnetons is 2.22 bohr magneon/atom\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "B=9.27*10**-24;      #bohr magneton(ampere m**2)\n",
    "a=2.86*10**-10;      #edge(m)\n",
    "Is=1.76*10**6;       #saturation value of magnetisation(ampere/m)\n",
    "\n",
    "#Calculation\n",
    "N=2/a**3;\n",
    "mew_bar=Is/N;      #number of Bohr magnetons(ampere m**2)\n",
    "mew_bar=mew_bar/B;      #number of Bohr magnetons(bohr magneon/atom)\n",
    "\n",
    "#Result\n",
    "print \"number of Bohr magnetons is\",round(mew_bar,2),\"bohr magneon/atom\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.5, Page number 6.47"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average magnetic moment is 2.79 *10**-3 bohr magneton/spin\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "mew0=4*math.pi*10**-7;\n",
    "H=9.27*10**-24;      #bohr magneton(ampere m**2)\n",
    "beta=10**6;      #field(ampere/m)\n",
    "k=1.38*10**-23;    #boltzmann constant\n",
    "T=303;    #temperature(K)\n",
    "\n",
    "#Calculation\n",
    "mm=mew0*H*beta/(k*T);    #average magnetic moment(bohr magneton/spin)\n",
    "\n",
    "#Result\n",
    "print \"average magnetic moment is\",round(mm*10**3,2),\"*10**-3 bohr magneton/spin\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.6, Page number 6.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hysteresis loss per cycle is 188.0 J/m**3\n",
      "hysteresis loss per second is 9400.0 watt/m**3\n",
      "power loss is 1.23 watt/kg\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "A=94;      #area(m**2)\n",
    "vy=0.1;    #value of length(weber/m**2)\n",
    "vx=20;     #value of unit length\n",
    "n=50;      #number of magnetization cycles\n",
    "d=7650;    #density(kg/m**3)\n",
    "\n",
    "#Calculation\n",
    "h=A*vy*vx;     #hysteresis loss per cycle(J/m**3)\n",
    "hs=h*n;       #hysteresis loss per second(watt/m**3)\n",
    "pl=hs/d;      #power loss(watt/kg)\n",
    "\n",
    "#Result\n",
    "print \"hysteresis loss per cycle is\",h,\"J/m**3\"\n",
    "print \"hysteresis loss per second is\",hs,\"watt/m**3\"\n",
    "print \"power loss is\",round(pl,2),\"watt/kg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.7, Page number 6.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= 5.43 Angstorm\n",
      "density = 6.88 kg/m**3\n",
      "#Answer given in the textbook is wrong\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#variable declaration\n",
    "d=2.351                 #bond lenght\n",
    "N=6.02*10**26           #Avagadro number\n",
    "n=8                     #number of atoms in unit cell\n",
    "A=28.09                 #Atomin mass of silicon\n",
    "m=6.02*10**26           #1mole\n",
    "\n",
    "#Calculations\n",
    "a=(4*d)/math.sqrt(3)\n",
    "p=(n*A)/((a*10**-10)*m)    #density\n",
    "\n",
    "#Result\n",
    "print \"a=\",round(a,2),\"Angstorm\"\n",
    "print \"density =\",round(p*10**16,2),\"kg/m**3\"\n",
    "print\"#Answer given in the textbook is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.8, Page number 6.48"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " radius of largest sphere is 0.154700538379252*r\n",
      "maximum radius of sphere is 0.414213562373095*r\n"
     ]
    }
   ],
   "source": [
    " import math\n",
    "from __future__ import division\n",
    "from sympy import Symbol\n",
    "\n",
    "#Variable declaration\n",
    "r=Symbol('r')\n",
    "\n",
    "#Calculation\n",
    "a1=4*r/math.sqrt(3);\n",
    "R1=(a1/2)-r;           #radius of largest sphere\n",
    "a2=4*r/math.sqrt(2);\n",
    "R2=(a2/2)-r;       #maximum radius of sphere\n",
    "\n",
    "#Result\n",
    "print \"radius of largest sphere is\",R1\n",
    "print \"maximum radius of sphere is\",R2    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.9, Page number 6.49"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a1= 2.905 Angstrom\n",
      "Unit cell volume =a1**3 = 24.521 *10**-30 m**3\n",
      "Volume occupied by one atom = 12.26 *10**-30 m**3\n",
      "a2= 3.654 Angstorm\n",
      "Unit cell volume =a2**3 = 48.8 *10**-30 m**3\n",
      "Volume occupied by one atom = 12.2 *10**-30 m**3\n",
      "Volume Change in % = 0.493\n",
      "Density Change in % = 0.5\n",
      "Thus the increase of density or the decrease of volume is about 0.5%\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#variable declaration\n",
    "r1=1.258            #Atomic radius of BCC\n",
    "r2=1.292            #Atomic radius of FCC\n",
    "\n",
    "#calculations\n",
    "a1=(4*r1)/math.sqrt(3)       #in BCC\n",
    "b1=((a1)**3)*10**-30         #Unit cell volume\n",
    "v1=(b1)/2                    #Volume occupied by one atom\n",
    "a2=2*math.sqrt(2)*r2         #in FCC\n",
    "b2=(a2)**3*10**-30           #Unit cell volume\n",
    "v2=(b2)/4                    #Volume occupied by one atom  \n",
    "v_c=((v1)-(v2))*100/(v1)     #Volume Change in % \n",
    "d_c=((v1)-(v2))*100/(v2)     #Density Change in %\n",
    "\n",
    "#Results\n",
    "print \"a1=\",round(a1,3),\"Angstrom\" \n",
    "print \"Unit cell volume =a1**3 =\",round((b1)/10**-30,3),\"*10**-30 m**3\"\n",
    "print \"Volume occupied by one atom =\",round(v1/10**-30,2),\"*10**-30 m**3\"\n",
    "print \"a2=\",round(a2,3),\"Angstorm\"\n",
    "print \"Unit cell volume =a2**3 =\",round((b2)/10**-30,3),\"*10**-30 m**3\"\n",
    "print \"Volume occupied by one atom =\",round(v2/10**-30,2),\"*10**-30 m**3\"\n",
    "print \"Volume Change in % =\",round(v_c,3)\n",
    "print \"Density Change in % =\",round(d_c,2)\n",
    "print \"Thus the increase of density or the decrease of volume is about 0.5%\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.10, Page number 6.50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= 0.563 *10**-9 metre\n",
      "spacing between the nearest neighbouring ions = 0.2814 nm\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#variable declaration\n",
    "n=4     \n",
    "M=58.5                  #Molecular wt. of NaCl\n",
    "N=6.02*10**26           #Avagadro number\n",
    "rho=2180                #density\n",
    "\n",
    "#Calculations\n",
    "a=((n*M)/(N*rho))**(1/3)    \n",
    "s=a/2\n",
    "\n",
    "#Result\n",
    "print \"a=\",round(a/10**-9,3),\"*10**-9 metre\"\n",
    "print \"spacing between the nearest neighbouring ions =\",round(s/10**-9,4),\"nm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.11, Page number 6.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lattice constant, a= 0.36 nm\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#variable declaration\n",
    "n=4     \n",
    "A=63.55                 #Atomic wt. of NaCl\n",
    "N=6.02*10**26           #Avagadro number\n",
    "rho=8930                #density\n",
    "\n",
    "#Calculations\n",
    "a=((n*A)/(N*rho))**(1/3)      #Lattice Constant\n",
    "\n",
    "#Result\n",
    "print \"lattice constant, a=\",round(a*10**9,2),\"nm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 6.12, Page number 6.51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Density of iron = 8805.0 kg/m**-3\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "r=0.123                  #Atomic radius\n",
    "n=4\n",
    "A=55.8                   #Atomic wt\n",
    "a=2*math.sqrt(2) \n",
    "N=6.02*10**26           #Avagadro number\n",
    "\n",
    "#Calculations\n",
    "rho=(n*A)/((a*r*10**-9)**3*N)\n",
    "\n",
    "#Result\n",
    "print \"Density of iron =\",round(rho),\"kg/m**-3\""
   ]
  }
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