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diff --git a/Applied_Physics-II_by_I_A_Shaikh/chapter6.ipynb b/Applied_Physics-II_by_I_A_Shaikh/chapter6.ipynb new file mode 100755 index 00000000..dec8353e --- /dev/null +++ b/Applied_Physics-II_by_I_A_Shaikh/chapter6.ipynb @@ -0,0 +1,1183 @@ +{ + "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": {} + } + ] +}
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