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 "worksheets": [

  {

   "cells": [

    {

     "cell_type": "heading",

     "level": 1,

     "metadata": {},

     "source": [

      "Chapter4:MAGNETIC PROPERTIES OF MATERIALS"

     ]

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg1:pg-153"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "import math\n",

      "phi_B=2.4e-5  #magnetic flux in weber\n",

      "A=0.2         #cross-sectional area in cm**2\n",

      "H=1600        #magnetising field in A/m\n",

      "mu_o=4*round(math.pi,2)*1e-7 #absolute permeability of air in N/A**2\n",

      "B=phi_B/(A*1e-4)\n",

      "mu=B/H\n",

      "Xm=mu/mu_o-1\n",

      "print\"Magnetic permeability of iron bar is \",\"{:.1e}\".format(mu),\"N/A**2\"\n",

      "print\"Magnetic susceptibility of iron bar is \",round(Xm,2)"

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Magnetic permeability of iron bar is  7.5e-04 N/A**2\n",

        "Magnetic susceptibility of iron bar is  596.13\n"

       ]

      }

     ],

     "prompt_number": 1

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg2:pg-154"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "from sympy import *\n",

      "Xm=948e-11      #magnetic susceptibility of a medium\n",

      "pi=Symbol('pi')\n",

      "mu_o=4*pi*1e-7  #absolute permeability of air in H/m\n",

      "mu_r=1+Xm\n",

      "mu=int(mu_r)*mu_o\n",

      "print\"Relative Permeability is =\",mu_r,\"=\",int(mu_r),\"or >\",int(mu_r)\n",

      "print\" Relative permeability is slightly greater than one.\"\n",

      "print\"Permeability is =\",mu,\"H/m\" #answer in book is 4*(pi)*1e-7 H/m"

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Relative Permeability is = 1.00000000948 = 1 or > 1\n",

        " Relative permeability is slightly greater than one.\n",

        "Permeability is = 4.0e-7*pi H/m\n"

       ]

      }

     ],

     "prompt_number": 1

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg3:pg-154"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "mu_r=1200 #relative permeability of iron rod\n",

      "n=5       #number of turns per cm\n",

      "i=0.5     #current in ampere\n",

      "V=1e-3    #volume of iron rod in m**3\n",

      "I=(mu_r-1)*(n*1e2)*i\n",

      "M=I*V\n",

      "print\"Magnetic moment is \",\"{:.0e}\".format(M),\"Am**2\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Magnetic moment is  3e+02 Am**2\n"

       ]

      }

     ],

     "prompt_number": 3

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg4:pg-155"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "import math\n",

      "mu_r=100  #relative permeability of iron rod\n",

      "n=300     #number of turns per meter\n",

      "i=0.5     #current in ampere\n",

      "D=10      #diameter of iron rod in mm\n",

      "r=D/2     #radius of iron rod in mm\n",

      "l=2       #length of iron rod in meter\n",

      "I=(mu_r-1)*n*i\n",

      "V=round(math.pi,2)*(r*1e-3)**2*l\n",

      "M=I*V\n",

      "print\"Magnetic moment is \",round(M,3),\"Am**2\"\n",

      "#answer in book is wrong as the value of l is taken wrong in calcultion.          "

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Magnetic moment is  2.331 Am**2\n"

       ]

      }

     ],

     "prompt_number": 4

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg5:pg-163"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "import math\n",

      "n=1e29        #number of atoms per unit volume in atoms/m**3\n",

      "Pm=1.8e-23    #magnetic moment of one atom in A-m**2\n",

      "K=1.38e-23    #Boltzmann's constant in J/K\n",

      "T=300         #temperature in Kelvin\n",

      "mu_o=4*round(math.pi,2)*10**-7 #absolute permeability of air in N/A**2\n",

      "B=0.1         #magnetic flux density in weber/m**2\n",

      "A=1           #cross-section area in cm**2\n",

      "l=10          #length of iron bar in cm\n",

      "Xm=mu_o*n*Pm**2/(3*K*T) #magnetic susceptibility of iron bar\n",

      "P_m=Pm**2*B/(3*K*T)     #mean dipole moment of an iron atom in A-m**2\n",

      "V=(A*1e-4)*(l*1e-2)     #volume of iron bar in m**3\n",

      "n_o_a=V*n               \n",

      "dm=n_o_a*P_m            #dipole moment of the iron bar \n",

      "I=Pm*n                  \n",

      "m=I*V\n",

      "print\"Magnetic Susceptibility is \",\"{:.3e}\".format(Xm)\n",

      "print\"Dipole moment is \",\"{:.3e}\".format(dm),\"Am**2\"\n",

      "print\"Magnetisation is \",\"{:.1e}\".format(I),\"A/m\"\n",

      "print\"Magnetic moment is \",int(m),\"Am**2\"#this answer is wrong in book"

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Magnetic Susceptibility is  3.277e-03\n",

        "Dipole moment is  2.609e-03 Am**2\n",

        "Magnetisation is  1.8e+06 A/m\n",

        "Magnetic moment is  18 Am**2\n"

       ]

      }

     ],

     "prompt_number": 5

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg6:pg-169"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "H=5e3  #Coercivity of bar magnet in ampere/m \n",

      "l=10   #length of solenoid in cm\n",

      "n=50   #number of turns in solenoid\n",

      "i=H*(l*1e-2)/n\n",

      "print\"Current is \",int(i),\"amp\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Current is  10 amp\n"

       ]

      }

     ],

     "prompt_number": 6

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg8:pg-170"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "a=250    #area of B-H loop in J/m**3\n",

      "f=50     #frequency of a.c. in Hz\n",

      "m=9.0    #mass of iron core in Kg\n",

      "p=7500   #density of iron in Kg/m**3\n",

      "V=m/p\n",

      "n=50*60*60\n",

      "E=n*V*a\n",

      "print\"Hysteresis loss of energy E per hour is \",\"{:.1e}\".format(E),\"J\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Hysteresis loss of energy E per hour is  5.4e+04 J\n"

       ]

      }

     ],

     "prompt_number": 7

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg10:pg-170"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "import math\n",

      "A=0.785e-4   #cross-sectional area of rowland ring in m**2\n",

      "Ri=5.0       #inner radius in cm\n",

      "Ro=6.0       #outer radius in cm\n",

      "N=400        #number of turns of wire\n",

      "Bo=2e-4      #magnetic flux density in weber/m**2\n",

      "mu_o=4*math.pi*10**-7 #absolute permeability of air in N/A**2\n",

      "Ns=50        #number of turns in secondary coil\n",

      "R=8.0        #resistance in ohm\n",

      "B1=800*Bo    #magnetic flux density in weber/m**2\n",

      "l=2*math.pi*(Ri+Ro)*1e-2/2\n",

      "i=Bo*l/(mu_o*N)\n",

      "q=Ns*B1*A/R\n",

      "print\"Required Current is \",i,\"amp\"\n",

      "print\"Charge passed is \",q,\"coulomb\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Required Current is  0.1375 amp\n",

        "Charge passed is  7.85e-05 coulomb\n"

       ]

      }

     ],

     "prompt_number": 8

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg11:pg-171"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "import math\n",

      "mu_r=400 #relative permeability of iron ring\n",

      "r=0.1    #mean radius of iron ring in meter\n",

      "A=5e-4   #cross-sectional area of iron ring in m**2\n",

      "n=1000   #number of turns of wire\n",

      "i=4      #current in ampere\n",

      "mu_o=4*math.pi*10**-7  #absolute permeability of air in N/A**2\n",

      "B=mu_o*mu_r*n*i/(2*math.pi*r)\n",

      "phi=B*A \n",

      "print\"Flux in the ring is \",\"{:.2e}\".format(phi),\"weber\"\n",

      "n_o=500  #number of turns in secondary coil per meter\n",

      "R=10     #resistance in ohm\n",

      "q=2*n_o*A*B/R\n",

      "print\"Electricity discharged through the secondary coil is \",q,\"coulomb\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Flux in the ring is  1.60e-03 weber\n",

        "Electricity discharged through the secondary coil is  0.16 coulomb\n"

       ]

      }

     ],

     "prompt_number": 9

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg12:pg-171"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "m=12    #weight of the iron core in Kg\n",

      "p=7.5   #density of iron core in gm/cc\n",

      "f=50    #frequency in cycles/sec\n",

      "a=3000  #area of hysteresis loop in ergs/cm**3 (unit is misprinted in question in book)\n",

      "V=(m*1e3)/p\n",

      "n=f*60*60\n",

      "E=n*V*a\n",

      "print\"Hourly loss of energy is \",E,\"erg\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Hourly loss of energy is  8.64e+11 erg\n"

       ]

      }

     ],

     "prompt_number": 10

    },

    {

     "cell_type": "heading",

     "level": 2,

     "metadata": {},

     "source": [

      "Eg13:pg-172"

     ]

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [

      "a=0.5   #area of B-H loop in cm**2\n",

      "H=1e3   #value of 1 cm on X-axis in A/m\n",

      "B=1     #value of 1 cm on Y-axis in Tesla\n",

      "V=1e-3  #volume of specimen in m**3\n",

      "n=50    #frequency of a.c. in Hz\n",

      "area=a*H*B #area of B-H loop in J/m**3 (this is misprinted in solution in book)\n",

      "p=n*V*area\n",

      "print\"Hysteresis power loss is \",int(p),\"Watt\""

     ],

     "language": "python",

     "metadata": {},

     "outputs": [

      {

       "output_type": "stream",

       "stream": "stdout",

       "text": [

        "Hysteresis power loss is  25 Watt\n"

       ]

      }

     ],

     "prompt_number": 11

    },

    {

     "cell_type": "code",

     "collapsed": false,

     "input": [],

     "language": "python",

     "metadata": {},

     "outputs": []

    }

   ],

   "metadata": {}

  }

 ]

}