diff options
Diffstat (limited to 'Engineering_Physics_Malik/Chapter_18.ipynb')
-rw-r--r-- | Engineering_Physics_Malik/Chapter_18.ipynb | 876 |
1 files changed, 876 insertions, 0 deletions
diff --git a/Engineering_Physics_Malik/Chapter_18.ipynb b/Engineering_Physics_Malik/Chapter_18.ipynb new file mode 100644 index 00000000..de6fffda --- /dev/null +++ b/Engineering_Physics_Malik/Chapter_18.ipynb @@ -0,0 +1,876 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 18: Magnetic Properties of Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.1, Page 18.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "r = 0.53e-10 # radius of orbit in m\n", + "f = 6.6e15 # frequency of revolution in Hz\n", + "h = 6.6e-34 # Planck constant in J sec\n", + "e = 1.6e-19 # charge on an electron in C\n", + "m = 9.1e-31 # mass of electron in kg\n", + "\n", + "#Calculations\n", + "M = e * f * pi * r**2\n", + "mu = (e * h) / (4 * pi * m) \n", + "\n", + "#Result\n", + "print \"Magnetic moment is %.3e Am^2\\nBohr magneton is %.2e J/T\"%(M,mu)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic moment is 9.319e-24 Am^2\n", + "Bohr magneton is 9.23e-24 J/T\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.2, Page 18.21" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = -4.2e-6 # magnetic susceptibility\n", + "H = 1.19e5 # magnetic field in A/m\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "I = X * H\n", + "B = mu_ * (H + I)\n", + "mur = (1 + I/H)\n", + "\n", + "#Results\n", + "print \"Magnetisation is %.2f A/m\\nFlux density is %.3f T\\nRelative permeability is %.2f\"%(I,B,mur)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetisation is -0.50 A/m\n", + "Flux density is 0.150 T\n", + "Relative permeability is 1.00\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.3, Page 18.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "X = 1.2e-5 # magnetic susceptibility of magnesium\n", + "\n", + "#Calculations\n", + "p = 100 * X\n", + "\n", + "#Result\n", + "print \"Percentage increase in magnetic induction is %.4f percent\"%p" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Percentage increase in magnetic induction is 0.0012 percent\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.4, Page 18.22" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = -0.4e-5 # magnetic susceptibility of material\n", + "H = 1e4 # magnetic field in A/m\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space\n", + "\n", + "#Calculations\n", + "I = X * H\n", + "B = mu_ * (H + I)\n", + "\n", + "#Result\n", + "print \"Magnetisation is %.2f A/m\\nMagnetic flux density is %f T\"%(I,B)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetisation is -0.04 A/m\n", + "Magnetic flux density is 0.012566 T\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.5, Page 18.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = 2.3e-5 # magnetic susceptibility of aluminium\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "mur = 1 + X\n", + "mu = mu_ * mur\n", + "\n", + "#Result\n", + "print \"Permeability of aluminium is %.2e N/A^2\"%mu" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permeability of aluminium is 1.26e-06 N/A^2\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.6, Page 18.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "X = 9.4e-2 # magnetic susceptibility\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "mu_r = 1 + X\n", + "mu = mu_ * mu_r\n", + "\n", + "#Results\n", + "print \"Absolute permeability is %.2e N/A^2\\nRelative permeability is %.3f\"%(mu,mu_r)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Absolute permeability is 1.37e-06 N/A^2\n", + "Relative permeability is 1.094\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.7, Page 18.23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "mu = 0.126 # maximum value of the permeability in N/A^2\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "mu_r = mu / mu_\n", + "X = mu_r - 1\n", + "\n", + "#Results\n", + "print \"Magnetic susceptibility is %.f\\nRelative permeability is %e\"%(X,mu_r)\n", + "#Answers differ due to rounding off values" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetic susceptibility is 100267\n", + "Relative permeability is 1.002676e+05\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.8, Page 18.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "r = 0.6e-10 # radius of the atom\n", + "N = 28e26 # no. of electron in per m^3\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "Z = 2 # atomic no. of helium\n", + "m = 9.1e-31 # mass of an electron in kg\n", + "e = 1.6e-19 # charge on an electron in C\n", + "\n", + "#Calculations\n", + "Chi = -(mu_ * Z * N * r**2 * e**2) / (6 * m)\n", + "\n", + "#Result\n", + "print \"Diamagnetic susceptibility is %.3e\"%Chi" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diamagnetic susceptibility is -1.188e-07\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.9, Page 18.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "H = 1e3 # magnetisation field in A/m\n", + "phi = 2e-5 # magnetic flux in Weber\n", + "a = 0.2e-4 # area of cross section in m^2\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "B = phi / a\n", + "mu = B / H\n", + "X = mu / mu_ - 1\n", + "\n", + "#Results\n", + "print \"Permeability is %.e N/A^2\\nSusceptibility is %.3f\"%(mu,X)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permeability is 1e-03 N/A^2\n", + "Susceptibility is 794.775\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.10, Page 18.24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 1 # length of iron rod in m\n", + "a = 4e-4 # area in m^2\n", + "mu = 50e-4 # permeability of iron in H/m\n", + "Phi = 4e-4 # magnetic flux in Weber\n", + "\n", + "#Calculations\n", + "B = Phi / a\n", + "NI = B / mu\n", + "\n", + "#Result\n", + "print \"Number of ampere turns is %d A/m\"%NI" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of ampere turns is 200 A/m\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.11, Page 18.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "n = 200 # no. of turns \n", + "l = 0.5 # the mean length of iron wire in m\n", + "phi = 4e-4 # magnetic flux in Weber\n", + "a = 4e-4 # area of cross section in m^2\n", + "mu = 6.5e-4 # permeability of iron in wb/Am\n", + "mu_ = 4 * pi * 1e-7 # magnetic permeability of space\n", + "\n", + "#Calculations\n", + "B = phi / a\n", + "N = n / l\n", + "I = B / (mu * N)\n", + "\n", + "#Result\n", + "print \"Current through the winding is %.2f A\"%I" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current through the winding is 3.85 A\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.12, Page 18.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "X = -5.6e-6 # magnetic susceptibility of material\n", + "a = 2.55e-10 # lattice constant in m\n", + "H = 1e4 # magnetic field in A/m\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space\n", + "m = 9.1e-31 # mass of electron in kg\n", + "e = 1.6e-19 # charge in an electron in C\n", + "\n", + "#Calculations\n", + "N = 2 / a**3\n", + "z = 1 \n", + "R = ((-X * 6 * m) / (mu_ * z * e**2 * N))**(1./2)\n", + "\n", + "#Result\n", + "print \"Radius of atom is %.2f A\"%(R * 1e10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Radius of atom is 0.89 A\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.13, Page 18.25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "N = 6.5e25 # no. of atom per m^3\n", + "T = 300 # room temperature in K\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space\n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "m = 9.1e-31 # mass of electron in kg\n", + "e = 1.6e-19 # charge in an electron in C\n", + "h = 6.62e-34 # Planck constant in J sec\n", + "\n", + "#Calculations\n", + "M = (e * h) / (4 * pi * m)\n", + "X = (mu_ * N * M**2) / (3 * k * T)\n", + "\n", + "#Result\n", + "print \"Susceptibility is %.3e\"%X" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Susceptibility is 5.642e-07\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.14, Page 18.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "w = 168.5 # molecular weight \n", + "d = 4370 # density of material in kg/m^3\n", + "H = 2e5 # magnetic field in A/m\n", + "T = 300 # room temperature in K\n", + "mu_ = 4 * pi * 1e-7 # magnetic permittivity of space]\n", + "NA = 6.02e26 # Avogadro no. in per kg\n", + "mu_b = 9.24e-24 # Bohr magnetons in Am^2\n", + "k = 1.38e-23 # Boltzmann's constant in J/K\n", + "\n", + "#Calculations\n", + "N = d * NA / w\n", + "X = (mu_ * N * (2 * mu_b)**2) / (3 * k * T)\n", + "I = X * H\n", + "\n", + "#Result\n", + "print \"Magnetisation is %.2f A/m\"%I" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Magnetisation is 107.89 A/m\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.15, Page 18.26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given that\n", + "A = 2500 # area of hysteresis loop \n", + "m = 10000 # weight in kg\n", + "d = 7.5 # density of material in g/cm^3\n", + "f = 50 # frequency in Hz\n", + "\n", + "#Calculations\n", + "E = f * A * 3600\n", + "V = m / d\n", + "L = E * V\n", + "\n", + "#Result\n", + "print \"Total loss of energy per hour is %.e ergs\"%L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total loss of energy per hour is 6e+11 ergs\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.16, Page 18.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "H = 5e3 # coercivity in A/m\n", + "l = 0.10 # length of solenoid in m\n", + "n = 50 # no. of turns \n", + "\n", + "#Calculations\n", + "N = n / l\n", + "i = H / N\n", + "\n", + "#Result\n", + "print \"Current in solenoid should be %d A\"%i" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current in solenoid should be 10 A\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.17, Page 18.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "l = 0.50 # length of iron rod in m\n", + "a = 4e-4 # area of cross section of rod in m^2\n", + "mu = 65e-4 # permeability of iron in H/m\n", + "fi = 4e-5 # flux in weber \n", + "\n", + "#Calculations\n", + "B = fi / a\n", + "H = B / mu\n", + "N = H * l\n", + "\n", + "#Result\n", + "print \"Number of turns are %.2f\"%N" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of turns are 7.69\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.18, Page 18.27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "H = 600 # magnetic flux in A/m\n", + "a = 0.2e-4 # area of cross section of rod in m^2\n", + "phi = 2.4e-5 # flux in weber \n", + "mu_ = 4*pi * 1e-7 # permeability of space in N/A^2\n", + "\n", + "#Calculations\n", + "B = phi / a\n", + "mu = B / H\n", + "X = mu / mu_ - 1\n", + "\n", + "#Result\n", + "print \"Permeability is %.3f N/A^2\\nSusceptibility is %.f\"%(mu,X)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Permeability is 0.002 N/A^2\n", + "Susceptibility is 1591\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.19, Page 18.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import *\n", + "\n", + "# Given \n", + "X = 9.5e-9 # susceptibility of medium \n", + "mu_ = 4*pi * 1e-7 # permeability of space in N/A^2\n", + "\n", + "#Calculations\n", + "mu = mu_ * (1 + X)\n", + "mu_r = mu / mu_\n", + "\n", + "#Result\n", + "print \"Relative permeability is 1 + %.3e\"%(mu_r -1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Relative permeability is 1 + 9.500e-09\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.20, Page 18.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "a = 250. # area of the B-H loop in J/m^3\n", + "f = 50. # frequency in Hz\n", + "d = 7.5e3 # density of iron in kg/m^3\n", + "m = 100. # mass of core in kg\n", + "\n", + "#Calculations\n", + "V = m / d\n", + "n = 3600 * f\n", + "A = a * V * n\n", + "\n", + "\n", + "#Result\n", + "print \"Energy loss per hour is %.3e J\"%A\n", + "#Answer varies due to rounding-off values" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Energy loss per hour is 6.000e+05 J\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 18.21, Page 18.28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + " \n", + "# Given \n", + "B_max = 1.375 # maximum value of B in Wb/m^2\n", + "a = 0.513 # area of the loop in cm^2\n", + "k = 1000 # value of 1 cm on x axis in A/m\n", + "k_ = 1 # value of 1 cm on y axis in Wb/m^2\n", + "B = 1.375 # alternating magnetic flux density in Wb/m^2\n", + "v = 1e-3 # volume of specimen in m^3\n", + "f = 50 # frequency in Hz\n", + "\n", + "#Calculations\n", + "K = a * k * k_\n", + "L = K * v * f\n", + "\n", + "#Result\n", + "print \"Hysteresis loss per sec is %.2f W\"%L" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hysteresis loss per sec is 25.65 W\n" + ] + } + ], + "prompt_number": 38 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |