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-{
- "metadata": {
- "celltoolbar": "Raw Cell Format",
- "name": "",
- "signature": "sha256:bc506d3130781232c57938d478c5c5179ee56efb068c1be93d57258ec96fcd79"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 6: Magnetic Materials and Circuits"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.1,Page number 2-26"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "H=198 #Magnetizing Force in Ampere per meter\n",
- "M=2300 #Magnetization in Ampere per meter\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "\n",
- "#Calculations:\n",
- "#H=(B/u0)-M\n",
- "B=u0*(H+M) #Flux Density\n",
- "ur=B/(u0*H) #Relative Permeability\n",
- "\n",
- "print\"Corresponding Flux Density is =\",B,\"Wb/m^2\"\n",
- "print\"Relative Permeability is =\",ur\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Corresponding Flux Density is = 0.00313907937947 Wb/m^2\n",
- "Relative Permeability is = 12.6161616162\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.2,Page number 2-26"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "x=3.7*10**-3 #Susceptibility at T=300 K\n",
- "T=300 #Temperature in kelvin\n",
- "T1=250 #Temperature in kelvin\n",
- "T2=600 #Temperature in kelvin\n",
- "\n",
- "#Calculations:\n",
- "C=x*T #Curie's law\n",
- "ur1=C/T1 #Relative permeability at 250 K\n",
- "ur2=C/T2 #Relative permeability at 600 K\n",
- "\n",
- "print\"Relative Permeability at 250 K is =\",ur1\n",
- "print\"Relative Permeability at 600 K is =\",ur2\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Relative Permeability at 250 K is = 0.00444\n",
- "Relative Permeability at 600 K is = 0.00185\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.3,Page number 2-27"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u=0.8*10**-23 #Magnetic dipole moment of an atom in paramagnetic gas in J/T\n",
- "B=0.8 #Magnetic field in tesla\n",
- "K=1.38*10**-23 #Boltzmann constant\n",
- "\n",
- "#To find Temperature at which Average thermal energy is equal to Magnetic energy \n",
- "#i.e. uB=3KT/2\n",
- "T=2*u*B/(3*K) #Required temperature\n",
- "\n",
- "print\"Required temperature is =\",T,\"Kelvin\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Required temperature is = 0.309178743961 Kelvin\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.4,Page number 2-27"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "T=27+273 #Temperature in kelvin\n",
- "B=0.5 #Magnetic field in tesla\n",
- "C=2*10**-3 #Curie's Constant\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "\n",
- "# C=u0*M*T/B (Curie's law)\n",
- "M=C*B/(u0*T) #Magnetization of material at 300 K\n",
- "\n",
- "print\"Magnetization of material at 300 K is =\",M,\"A/m\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnetization of material at 300 K is = 2.65258238486 A/m\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.5,Page number 2-27"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "B=10.9*10**-5 #Horizontal component of B in wb/m^2\n",
- "u0=4*math.pi*10**-7 #Permeability in free space\n",
- "\n",
- "H=B/u0 #Horizontal component of magnetic field\n",
- "print\"Horizontal component of magnetic field is =\",H,\"Ampere/meter\"\n",
- "print\"(Print mistake in unit in book)\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Horizontal component of magnetic field is = 86.7394439851 Ampere/meter\n",
- "(Print mistake in unit in book)\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.6,Page number 2-28"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=900 #Relative permeability of medium\n",
- "l=2 #length in meter\n",
- "A=60*10**-4 #Crosss sectional area of ring in m^2\n",
- "phi=5.9*10**-3 #flux in weber\n",
- "n=700 #Number of turns\n",
- "\n",
- "#Calculations:\n",
- "#We know, phi=B*A\n",
- "B=phi/A #Flux density\n",
- "#But, B=u*H\n",
- "H=B/(u0*ur) #Magnetic field strength\n",
- "\n",
- "I=H*l/n #Required current\n",
- "print\"Current required to produce given flux is =\",I,\"Ampere\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Current required to produce given flux is = 2.48416445567 Ampere\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.7,Page number 2-28"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=900 #Relative permeability of medium\n",
- "r=25*10**-2 #radius of ring\n",
- "A=25*10**-4 #Crosss sectional area of ring in m^2\n",
- "Ag=1*10**-3 #Air gap\n",
- "phi=2.7*10**-3 #flux in weber\n",
- "N=400 #Number of turns\n",
- "\n",
- "#Calculations:\n",
- "#We know, phi=B*A\n",
- "B=phi/A #Flux density\n",
- "#But, B=u*H\n",
- "H=B/(u0*ur) #Magnetic field strength\n",
- "L=H*2*math.pi*r+(B*Ag/u0) #Total amp turns required (iron+air)\n",
- "I=L/N #Required current\n",
- "\n",
- "print\"Current required to produce given flux is =\",I,\"Ampere\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Current required to produce given flux is = 5.89859173174 Ampere\n"
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.8,Page number 2-29"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "A=0.2*10**-4 #Crosss sectional area of iron bar in m^2\n",
- "H=1600 #magnetising field in A/m\n",
- "phi=2.4*10**-5 #Magnetic flux in weber\n",
- "\n",
- "\n",
- "#Calculations:\n",
- "#We know, phi=B*A\n",
- "B=phi/A #Flux density\n",
- "u=B/H #magnetic permeability\n",
- "ur=u/u0 #relative permeability\n",
- "xm=ur-1 #susceptibility of the iron bar\n",
- "\n",
- "print\"magnetic permeability of iron bar is =\",u,\"N/(A^2)\"\n",
- "print\"susceptibility of the iron bar is =\",xm\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "magnetic permeability of iron bar is = 0.00075 N/(A^2)\n",
- "susceptibility of the iron bar is = 595.831036595\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.9,Page number 2-29"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "xm=948*10**-11 #susceptibility of the iron bar\n",
- "\n",
- "#Calculations:\n",
- "ur=1+xm #relative permeability\n",
- "u=u0*ur #permeability of medium\n",
- "\n",
- "print\"Relative Permeability of medium is =\",ur\n",
- "print\"Permeability of medium is =\",u,\"H/m\"\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Relative Permeability of medium is = 1.00000000948\n",
- "Permeability of medium is = 1.25663707335e-06 H/m\n"
- ]
- }
- ],
- "prompt_number": 13
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.10,Page number 2-30"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "B=2.5 #Magnetic field in tesla\n",
- "u0=4*math.pi*10**-7 #Permeability in free space\n",
- "i0=0.7 #current in the core\n",
- "ri=11*10**-2 #inner radii of core\n",
- "ro=12*10**-2 #outer radii of core\n",
- "\n",
- "#Calculations:\n",
- "r=(ri+ro)/2 #Average radii of core\n",
- "n=3000/(2*math.pi*r) #Number of turns\n",
- "\n",
- "#We know, B=u0*ur*n*i0 .Thus,\n",
- "ur=B/(u0*n*i0)\n",
- "\n",
- "print\"Relative Permeability of medium is =\",ur\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Relative Permeability of medium is = 684.523809524\n"
- ]
- }
- ],
- "prompt_number": 14
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.11,Page number 2-31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "B=1.0 #Flux density in tesla\n",
- "u0=4*math.pi*10**-7 #Permeability in free space\n",
- "i=2.0 #current in the core\n",
- "n=10*100 #n=N/l i.e. turns per meter\n",
- "\n",
- "#Calculations:\n",
- "H=n*i #Magnetising force produced in wire\n",
- "print\"Magnetising force produced in wire is =\",H,\"Amp-turn/meter\"\n",
- "\n",
- "#We know that, B=u0(H+I).Thus,\n",
- "I=B/u0-H #Magnetisation of material\n",
- "print\"Magnetisation of material is =\",I,\"Amp-turn/meter\"\n",
- "\n",
- "#u=B/H, i.e. ur*u0=B/H.\n",
- "ur=B/(u0*H) #Relative permeability of core\n",
- "print\" Relative Permeability of core is =\",ur\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnetising force produced in wire is = 2000.0 Amp-turn/meter\n",
- "Magnetisation of material is = 793774.715459 Amp-turn/meter\n",
- " Relative Permeability of core is = 397.88735773\n"
- ]
- }
- ],
- "prompt_number": 15
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.12,Page number 2-31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "M=40 #Mass of an iron core\n",
- "D=7.5*10**3 #Density of iron\n",
- "f=100 #Frequency\n",
- "A=3800*10**-1 #Loss due to Area of hysterisis loop in J/m^3\n",
- "\n",
- "#Calculations:\n",
- "V=M/D #Volume of iron core\n",
- "L1=A*V #Loss of energy in core per cycle\n",
- "print\"Loss of energy in core per cycles is =\",L1,\"joules\"\n",
- "\n",
- "N=f*60 #Number of cycles per minute\n",
- "L=L1*N #Loss of energy per minute\n",
- "\n",
- "print\"Loss of energy per minute is =\",L,\"joules\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Loss of energy in core per cycles is = 2.02666666667 joules\n",
- "Loss of energy per minute is = 12160.0 joules\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.13,Page number 2-32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "l=30*10**-2 #length in meter\n",
- "A=1*10**-4 #Crosss sectional area of ring in m^2\n",
- "phi=2*10**-6 #flux in weber\n",
- "N=300 #Number of turns\n",
- "I=0.032 #Current in winding\n",
- "\n",
- "#Calculations:\n",
- "#(i):\n",
- "B=phi/A #Flux density\n",
- "print\"(i)Flux Density in the ring is =\",B,\"Wb/m^2\"\n",
- "\n",
- "#(ii):\n",
- "H=N*I/l #Magnetic intensity\n",
- "print\"(ii)Magnetic intensity is =\",H,\"Amp-turn/meter\"\n",
- "\n",
- "#(iii):\n",
- "u=B/H #Permeability of ring\n",
- "print\"(iii)Permeability of ring is =\",u,\" Wb/A-m\"\n",
- "ur=u/u0 #Relative permeability of ring\n",
- "print\"Relative Permeability of ring is =\",ur\n",
- "\n",
- "#(iv):\n",
- "xm=ur-1 #susceptibility of the ring\n",
- "print\"(iv)Magnetic susceptibility of the ring is =\",xm\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "(i)Flux Density in the ring is = 0.02 Wb/m^2\n",
- "(ii)Magnetic intensity is = 32.0 Amp-turn/meter\n",
- "(iii)Permeability of ring is = 0.000625 Wb/A-m\n",
- "Relative Permeability of ring is = 497.359197162\n",
- "(iv)Magnetic susceptibility of the ring is = 496.359197162\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.14,Page number 2-32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Dta:\n",
- "M=12*10**3 #Mass of an iron core in grams\n",
- "D=7.5 #Density of iron in gm/cc\n",
- "f=50 #Frequency\n",
- "A=3000 #loss due to Area of hysterisis loop in ergs/cm^3\n",
- "\n",
- "#Calculations:\n",
- "V=M/D #Volume of iron core\n",
- "L1=A*V #Loss of energy in core per cycle\n",
- "\n",
- "L=L1*f*3600 #Loss of energy per hour\n",
- "\n",
- "print\"Loss of energy per hour is =\",L,\"Erg\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Loss of energy per hour is = 8.64e+11 Erg\n"
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.15,Page number 2-33"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "A=0.5*10**3 #Area of B-H loop in Joules per m^3\n",
- "V=10**-3 #Volume of specimen in m^3\n",
- "n=50 #Frequency of a.c.\n",
- "\n",
- "#Calculations:\n",
- "H=n*V*A #Hysteresis power loss\n",
- "\n",
- "print\"Hysteresis power loss is =\",H,\"Watt\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Hysteresis power loss is = 25.0 Watt\n"
- ]
- }
- ],
- "prompt_number": 19
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.16,Page number 2-33"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=1000 #Relative permeability of medium\n",
- "V=10**-4 #Volume of iron rod in m^3\n",
- "n=500 #Number of turns per meter\n",
- "i=0.5 #Current in windings of solenoid in Amperes\n",
- "\n",
- "#Calculations:\n",
- "#We know I=(ur-1)H\n",
- "#and H=ni , hence\n",
- "I=(ur-1)*n*i #Intensity of magnetisation\n",
- "M=I*V #Magnetic moment\n",
- "\n",
- "print\"Magnetic moment of the rod is =\",M,\"A-m^2\"\n",
- "\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnetic moment of the rod is = 24.975 A-m^2\n"
- ]
- }
- ],
- "prompt_number": 22
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.17,Page number 2-34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=600 #Relative permeability of iron\n",
- "d=12*10**-2 #mean diameter of ring in m\n",
- "N=500 #Number of turns\n",
- "i=0.3 #Current in windings of solenoid in Amperes\n",
- "\n",
- "#Calculations:\n",
- "r=d/2 #Radius of ring\n",
- "\n",
- "B=u0*ur*N*i/(2*math.pi*r) #Flux densityin the core\n",
- "print\"Flux densityin the core is =\",B,\"Wb/m^2\"\n",
- "\n",
- "H=B/(u0*ur) #Magnetic intensity\n",
- "print\"Magnetic intensity is =\",H,\"Amp-turns/m\"\n",
- "\n",
- "#We know that, B=u0(H+I)\n",
- "I1=(B-u0*H)/u0 #magnetisation\n",
- "I2=u0*I1 #Electronic current loop\n",
- "\n",
- "I=I2/B*100 #Percentage flux density due to electroniuc loop currents\n",
- "print\"Percentage flux density due to electroniuc loop currents is =\",I,\"percent\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Flux densityin the core is = 0.3 Wb/m^2\n",
- "Magnetic intensity is = 397.88735773 Amp-turns/m\n",
- "Percentage flux density due to electroniuc loop currents is = 99.8333333333 percent\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.18,Page number 2-35"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=900 #Relative permeability of iron ring\n",
- "d=40*10**-2 #diameter of ring\n",
- "l=5*10**-3 #air gap in the ring\n",
- "A=5.8*10**-4 #Crosss sectional area of ring in m^2\n",
- "phi=1.5*10**-4 #flux in weber\n",
- "N=600 #Number of turns\n",
- "\n",
- "#Calculations:\n",
- "r=d/2 #Radius of ring\n",
- "\n",
- "#We know, phi=B*A\n",
- "B=phi/A #Flux density\n",
- "\n",
- "#But, B=u*H\n",
- "H=B/(u0*ur) #Magnetic field strength\n",
- "\n",
- "m1=H*ur*l #amp-turns in air gap\n",
- "m2=H*2*math.pi*r #amp-turns by ring\n",
- "m=m1+m2 #total mmf(amp-turns) required\n",
- "\n",
- "I=m/N #Required current\n",
- "print\"Current required to produce given flux is =\",I,\"Amperes\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Current required to produce given flux is = 2.19395891742 Amperes\n"
- ]
- }
- ],
- "prompt_number": 24
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.18.1,Page number 2-38"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "X=-0.5*10**-5 #Magnetic susceptibility of silicon\n",
- "H=9.9*10**4 #Magnetic field intensity\n",
- "\n",
- "#Calculations:\n",
- "\n",
- "#As, X=I/H. thus,\n",
- "I=X*H #intensity of magnetisation\n",
- "print\"Intensity of magnetisation is =\",I\n",
- "\n",
- "B=u0*(H+I) #Magnetic flux density\n",
- "print\"Magnetic flux density is =\",B,\"Wb/ m^2\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Intensity of magnetisation is = -0.495\n",
- "Magnetic flux density is = 0.124406447047 Wb/ m^2\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.18.2,Page number 2-38"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=380 #Relative permeability\n",
- "d=20*10**-2 #diameter of solenoid in m\n",
- "r=d/2 #radius of ring in m\n",
- "A=5*10**-4 #Crosss sectional area of ring in m^2\n",
- "phi=2*10**-3 #flux in weber\n",
- "N=200 #Number of turns\n",
- "\n",
- "#Calculations:\n",
- "l=math.pi*d #air gap in the ring\n",
- "S=(l/(u0*ur*A)) #Reluctance of iron ring\n",
- "print\"Reluctance of iron ring is =\",S,\"Amp-turn/ Wb \"\n",
- "\n",
- "#ohm's law for magnetic circuit is phi=N*I/S. thus,\n",
- "I=S*phi/N #required current\n",
- "print\"Current required to obtain given magnetic flux is =\",I,\"Amperes\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Reluctance of iron ring is = 2631578.94737 Amp-turn/ Wb \n",
- "Current required to obtain given magnetic flux is = 26.3157894737 Amperes\n"
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.18.3,Page number 2-39"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Values:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=1 #Relative permeability of air\n",
- "r=15*10**-2 #radius of ring in m\n",
- "A=6*10**-4 #Crosss sectional area of ring in m^2\n",
- "I=4 #Coil current in amp\n",
- "N=500 #Number of turns\n",
- "\n",
- "#Calculations:\n",
- "m=N*I #MMF of coil\n",
- "print\"MMF of coil is =\",m,\"Ampere-turn\"\n",
- "\n",
- "l=2*math.pi*r #air gap\n",
- "R=(l/(u0*ur*A)) #Reluctance of iron ring\n",
- "print\"Reluctance of iron ring is =\",R,\"Ampere-turn/Wb\"\n",
- "\n",
- "phi=m/R #Magnetic flux\n",
- "print\"Magnetic flux is =\",phi,\"Weber\"\n",
- "\n",
- "B=phi/A #Magnetic Flux density\n",
- "print\"Magnetic flux density is =\",B,\"Weber/m^2\"\n",
- "\n",
- "H=B/(u0*ur) #Magnetic field intensity\n",
- "print\"Magnetic field intensity is =\",H,\"Amperes/m\"\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "MMF of coil is = 2000 Ampere-turn\n",
- "Reluctance of iron ring is = 1250000000.0 Ampere-turn/Wb\n",
- "Magnetic flux is = 1.6e-06 Weber\n",
- "Magnetic flux density is = 0.00266666666667 Weber/m^2\n",
- "Magnetic field intensity is = 2122.06590789 Amperes/m\n"
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.19,Page number 2-36"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "u0=4*math.pi*10**-7 #Permeability in vacuum\n",
- "ur=6*10**-3 #Relative permeability of iron\n",
- "r=0.5 #radius of ring in m\n",
- "l=1*10**-2 #air gap in the ring\n",
- "A=5*10**-4 #Crosss sectional area of ring in m^2\n",
- "i=5 #current in ampere\n",
- "N=900 #Number of turns\n",
- "\n",
- "#Calculations:\n",
- "S=(l/(u0*A))+((2*math.pi*r-l)/ur*A) #Reluctance of iron\n",
- "print\"Reluctance of iron is =\",S,\"Ampere-turn/Wb\"\n",
- "\n",
- "m=N*i #mmf produced\n",
- "print\"mmf produced is =\",m,\"Ampere-turn\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Reluctance of iron is = 15915494.5702 Ampere-turn/Wb\n",
- "mmf produced is = 4500 Ampere-turn\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.20,Page number 2-36"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "H=5*10**3 #coercivity of bar magnet in amp/m\n",
- "l=10*10**-2 #length of solenoid in m\n",
- "N=50 #No of turns\n",
- "\n",
- "#Calculations:\n",
- "\n",
- "#We know that, H=NI/l ,hence\n",
- "I=l*H/N #current through solenoid\n",
- "\n",
- "print\"Current through solenoid is =\",I,\"Amperes\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Current through solenoid is = 10.0 Amperes\n"
- ]
- }
- ],
- "prompt_number": 30
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.21,Page number 2-36"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "ur=1200 #Relative permeability of medium\n",
- "V=10**-3 #volume of iron rod\n",
- "N=5*10**2 #no of turns per m\n",
- "i=0.5 #current through solenoid in amp\n",
- "\n",
- "#Calculations:\n",
- "x=ur-1 #susceptibility of the ring\n",
- "H=N*i #Magnetisisng field\n",
- "\n",
- "#We know, x=I/H\n",
- "I=x*H #magnetisation\n",
- "\n",
- "#Also, I=M/V , thus\n",
- "M=I*V #magnetic moment\n",
- "print\"Magnetic moment is =\",M,\"Ampere-turn-m^2\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnetic moment is = 299.75 Ampere-turn-m^2\n"
- ]
- }
- ],
- "prompt_number": 31
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.22,Page number 2-37"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Dta:\n",
- "ur=100 #Relative permeability of medium\n",
- "l=0.2 #length of iron rod\n",
- "d=10*10**-3 #diameter of solenoid in m\n",
- "N=300 #no of turns per m\n",
- "i=0.5 #current through solenoid in amp\n",
- "r=d/2 #radius of solenoid\n",
- "\n",
- "#Calculations:\n",
- "x=ur-1 #susceptibility of the ring\n",
- "H=N*i #Magnetisisng field\n",
- "\n",
- "#We know, x=I/H\n",
- "I=x*H #magnetisation\n",
- "\n",
- "V=math.pi*(r**2)*l #volume of iron rod\n",
- "\n",
- "#Also, I=M/V , thus\n",
- "M=I*V #magnetic moment\n",
- "print\"Magnetic moment is =\",M,\"Ampere-turn-m^2\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnetic moment is = 0.233263254529 Ampere-turn-m^2\n"
- ]
- }
- ],
- "prompt_number": 33
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 6.23,Page number 2-38"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Given Data:\n",
- "l=1.2 #length of circuit in meter\n",
- "u=7.3*10**-3 #permeability of silicon sheet\n",
- "A=100 #cross sectional area in cm^2\n",
- "N=150 #No of turns\n",
- "B=0.3 #magmetic field in Wb/m^2\n",
- "\n",
- "#Calculations:\n",
- "\n",
- "#We know, B=u*H\n",
- "H=B/u #Magnetic field strength\n",
- "\n",
- "m=H*l #amp-turns in air gap\n",
- "\n",
- "I1=m/N #Required current\n",
- "print\"Current required to obtain given magnetic field is =\",I1,\"Amperes\"\n",
- "\n",
- "I=I1/A #Required current per unit area\n",
- "print\"Current required per unit area to obtain given magnetic field is =\",I,\"Amperes\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Current required to obtain given magnetic field is = 0.328767123288 Amperes\n",
- "Current required per unit area to obtain given magnetic field is = 0.00328767123288 Amperes\n"
- ]
- }
- ],
- "prompt_number": 34
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-23 19:00:02 +0000