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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Capter 19: Magnetic Materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.1, page no-541"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Relative permiability and magnetic force\n",
"\n",
"import math\n",
"#Variable Declaration\n",
"M=2300.0 # Magnetization\n",
"B=0.00314 # Flux density\n",
"\n",
"#Calculation\n",
"mu=4*math.pi*10**-7\n",
"H=(B/mu)-M\n",
"mur=(M/H)+1\n",
"\n",
"#Result\n",
"print('The magnetic force H is %.4f A/m and the relative permeability mu_r is %.5f'%(H,mur))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetic force H is 198.7326 A/m and the relative permeability mu_r is 12.57334\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.2, page no-542"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# magnetisation and flux density\n",
"\n",
"import math\n",
"#Variable Declaration\n",
"H=10**4 # Magnetic field intensity\n",
"sus=3.7*10**-3 # Susceptibility\n",
"mu=4*math.pi*10**-7 # permeability of free space\n",
"\n",
"#Calculation\n",
"M=sus*H\n",
"B=mu*(M+H)\n",
"\n",
"#Result\n",
"print('The magnetisation in the material is %.0f A/m and flux density in the material is %.2f * 10^-2 Wb.m^-2'%(M,B*10**2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetisation in the material is 37 A/m and flux density in the material is 1.26 * 10^-2 Wb.m^-2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.3, page no-542"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Flux density in a material\n",
"\n",
"import math\n",
"#variable declaration\n",
"H=10**4 # Magnetic field intensity \n",
"sus=-0.8*10**-5 # susceptibility of copper\n",
"mu=4*math.pi*10**-7 # permeability of free space\n",
"\n",
"#Calculations\n",
"M=sus*H\n",
"B=mu*(M+H)\n",
"\n",
"#Result\n",
"print('The flux density in the material is %.2f * 10^-2 Wb.m^-2'%(B*10**2))\n",
"\n",
"# Magnetic field intensity: value given in the book is 10^6 but calculations are done with 10^4"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The flux density in the material is 1.26 * 10^-2 Wb.m^-2\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.4, page no-543"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Permeability \n",
"\n",
"import math\n",
"# Variable declarations\n",
"H=1800.0 # Magnetic field intensity\n",
"fi=3*10**-5 # Magnetic flux\n",
"A=0.2*10**-4 # Area of cross-section \n",
"\n",
"#Calculations\n",
"B=fi/A\n",
"mu=B/H\n",
"\n",
"#Result\n",
"print('\\nThe magnetic flux is %.1f Wb/m^2\\nThe permeability is %.3f*10^-4 H/m'%(B,mu*10**4))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The magnetic flux is 1.5 Wb/m^2\n",
"The permeability is 8.333*10^-4 H/m\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.5, page no-544"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Magnetic moment of Nickel\n",
"\n",
"import math\n",
"#variable declaration\n",
"B=0.65 # Magnetic inductionof Nickel\n",
"r=8906 # Density of Nickel\n",
"M=58.7 # Atomic weight\n",
"avg=6.023*10**26 # Avogadro's Number\n",
"mu=4*math.pi*10**-7 # Permeability of free space\n",
"k=9.27*10**-24 # 1 Bohr Magnetron\n",
"\n",
"#Calculations\n",
"N=r*avg/M \n",
"mu_m=B/(N*mu)\n",
"mu_m=mu_m/k\n",
"\n",
"#Result\n",
"print(\"The magnetic moment of nickel atom is %.2f Bohr magneton\"%mu_m)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetic moment of nickel atom is 0.61 Bohr magneton\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.6, page no-545"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Average magnetization contributed per atom\n",
"\n",
"import math\n",
"# Variable declaration\n",
"a=2.5*10**-10 # interatomic spacing\n",
"M=1.8*10**6 # MAgnetization\n",
"e=1.6*10**-19 # charge of an electron\n",
"\n",
"#Calculations\n",
"n=2/a**3\n",
"m=9.1*10**-31\n",
"h=6.625*10**-34\n",
"ma=M/n\n",
"beta1=e*h/(4*math.pi*m)\n",
"\n",
"#Result\n",
"print(\"The average magnetisation contributed per atom = %.3f Bohr Magneton\"%(ma/beta1))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average magnetisation contributed per atom = 1.517 Bohr Magneton\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.7, page no-545"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Tempoerature using classical statistics\n",
"\n",
"import math\n",
"#Variable declarations\n",
"mu=9.4*10**-24 # Permeability \n",
"H=2 # MAgnetic field intensity\n",
"k=1.38*10**-23 # Bolzmann's constant\n",
"\n",
"#Calculations\n",
"T=2*mu*H/(k*math.log(2))\n",
"\n",
"#Result\n",
"print(\"The temperature of the system T is %.1f K\"%T)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The temperature of the system T is 3.9 K\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.8, page no-547"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Saturation magnetic field of Gd atom\n",
"\n",
"import math\n",
"#Variable declaration\n",
"ba=7.1 # Bohr magnetron per atom\n",
"aw=1.8*10**6 # Atomic weight of Gd \n",
"d=7.8*10**3 # Density of Gd\n",
"avg=6.023*10**26 # Avogadro's Number\n",
"M=157.26 # Atomic number of Gd\n",
"k=9.27*10**-24 # 1 Bohr magnetron\n",
"mu=4*math.pi*10**-7 # permeability of free space\n",
"\n",
"\n",
"#Calculations\n",
"N=d*avg/M\n",
"mm=N*ba*k\n",
"B=N*mu*k*7.1\n",
"\n",
"#Result\n",
"print(\"\\nThe saturation magnetic field of Gd atom is %.2f Wb/m^2\"%B)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The saturation magnetic field of Gd atom is 2.47 Wb/m^2\n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.9, page no-547"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#saturation magnetisation\n",
"\n",
"import math\n",
"# variable ddeclaration\n",
"bet=9.27*10**-24 # 1 Bohr magnetron\n",
"V=0.839*10**-9 # unit cell edge length\n",
"\n",
"#Calculations\n",
"M=32*bet/V**3\n",
"\n",
"#Result\n",
"print(\"The saturation magnetisation is %.3f *10^5 A/m\"%(M*10**-5))\n",
"# Answer in the book is given as 5.023 x 10^-5"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The saturation magnetisation is 5.023 *10^5 A/m\n"
]
}
],
"prompt_number": 55
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.10, page no-548"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Saturation flux density\n",
"\n",
"import math\n",
"#variable declaration\n",
"d=8900 # Density of Ni\n",
"wt=58.71 # Atomic weight\n",
"avg=6.022*10**26 # Avogadro's Number\n",
"bet=9.27*10**-24 # 1 Bohr magnetron\n",
"mu=4*math.pi*10**-7 # permeability of free space\n",
"\n",
"#Calculations\n",
"mm=0.6*bet\n",
"N=d*avg/wt\n",
"ms=mm*N\n",
"bs=mu*ms\n",
"\n",
"#Result\n",
"print(\"\\nThe saturation magnetisation is %.3f *10^5 A/m\\nThe saturation flux density is %.3f Wb/m^2\"%(ms*10**-5,bs))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The saturation magnetisation is 5.077 *10^5 A/m\n",
"The saturation flux density is 0.638 Wb/m^2\n"
]
}
],
"prompt_number": 57
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.11, page no-548"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Saturation magnetisation of gadolinium\n",
"\n",
"import math\n",
"#variable declaration\n",
"awt=157.25 # Atomic weight\n",
"an=64 # Atomic number\n",
"d=7860 # density\n",
"k=9.27*10**-24 # 1 Bohr magnetron\n",
"avg=6.023*10**26 # avogadro's Number\n",
"\n",
"#Calculations\n",
"N=d*8*k*avg/awt\n",
"\n",
"# Result\n",
"print(\"The saturation magnetisation of gadolinium is %.2f*10^6 A/m\"%(N*10**-6))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The saturation magnetisation of gadolinium is 2.23*10^6 A/m\n"
]
}
],
"prompt_number": 58
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.12, page no-549"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Magnetic flux density inside the material\n",
"\n",
"import math\n",
"#variable declaration\n",
"H=1000 # Magnetic field strength\n",
"sus=-0.3*10**-5 # magnetic susceptibility\n",
"mu=4*math.pi*10**-7 # permeability of free space\n",
"\n",
"#calculation\n",
"M=sus*H\n",
"B=mu*(M+H)\n",
"B=math.floor(B*10**6)/10**6\n",
"\n",
"#Result\n",
"print(\"The magnetic flux density inside the material is %.3f T or Wb.m^-2\"%(B*10**3))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetic flux density inside the material is 1.256 T or Wb.m^-2\n"
]
}
],
"prompt_number": 67
}
],
"metadata": {}
}
]
}