{
"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": {}
}
]
}