{ "metadata": { "name": "", "signature": "sha256:3eb552fb3c1a7764bbfbba83330f0d6a18ee201068631d5f4e4579961984a5eb" }, "nbformat": 3, "nbformat_minor": 0, "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": {} } ] }