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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"14: Magnetic Properties of Materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.1, Page number 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N = 6.02*10**23; #Avogadro's number(per mole)\n",
"A = 56; #Atomic weight of the substance(g/mole)\n",
"d = 7.9; #Density of the substance(g/cm**3)\n",
"m_B = 9.27*10**-24; #Bohr's Magneton(J/T)\n",
"\n",
"#Calculation\n",
"m = 2.2*m_B; #Magnetic moment of substance(J/T)\n",
"n = d*N/A ; #Number of atoms per unit volume of the substance(per cm**3)\n",
"n = n*10**6; #Number of atoms per unit volume of the substance(per m**3)\n",
"M = n*m; #Spontaneous magnetisation of the substance(A/m)\n",
"M = M/10**6;\n",
"M = math.ceil(M*10**3)/10**3; #rounding off the value of M to 3 decimals\n",
"\n",
"#Result\n",
"print \"The spontaneous magnetisation of the substance is\",M,\"*10**6 A/m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The spontaneous magnetisation of the substance is 1.732 *10**6 A/m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.2, Page number 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"H = 200; #Field strength to which the ferromagnetic material is subjected(A/m)\n",
"M = 3100; #Magnetisation of the ferromagnetic material(A/m)\n",
"\n",
"#Calculation\n",
"chi = M/H; #Magnetic susceptibility\n",
"mew_r = 1 + chi; #Relative permeability of ferromagnetic material\n",
"\n",
"#Result\n",
"print \"The relative permeability of ferromagnetic material is\",mew_r"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The relative permeability of ferromagnetic material is 16.5\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.3, Page number 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"H = 300; #Field strength to which the ferromagnetic material is subjected(A/m)\n",
"M = 4400; #Magnetisation of the ferromagnetic material(A/m)\n",
"\n",
"#Calculation\n",
"chi = M/H; #Magnetic susceptibility\n",
"mew_r = 1 + chi; #Relative permeability of ferromagnetic material\n",
"mew_r = math.ceil(mew_r*100)/100; #rounding off the value of mew_r to 2 decimals\n",
"\n",
"#Result\n",
"print \"The relative permeability of ferromagnetic material is\",mew_r\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The relative permeability of ferromagnetic material is 15.67\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.4, Page number 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"\n",
"#Variable declaration\n",
"mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n",
"H = 10000; #Field strength to which the diamagnetic material is subjected(A/m)\n",
"chi = -0.4*10**-5; #Magnetic susceptibility\n",
"\n",
"#Calculation\n",
"M = chi*H; #Magnetisation of the diamagnetic material(A/m)\n",
"B = mew_0*(H + M); #Magnetic flux density of diamagnetic material(T)\n",
"B = math.ceil(B*10**4)/10**4; #rounding off the value of B to 4 decimals\n",
"\n",
"#Result\n",
"print \"The magnetisation of diamagnetic material is\",M, \"A/m\"\n",
"print \"The magnetic flux density of diamagnetic material is\",B, \"T\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetisation of diamagnetic material is -0.04 A/m\n",
"The magnetic flux density of diamagnetic material is 0.0126 T\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.5, Page number 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n",
"H = 1.2*10**5; #Field strength to which the diamagnetic material is subjected(A/m)\n",
"chi = -4.2*10**-6; #Magnetic susceptibility\n",
"\n",
"#Calculation\n",
"M = chi*H; #Magnetisation of the diamagnetic material(A/m)\n",
"B = mew_0*(H + M); #Magnetic flux density of diamagnetic material(T)\n",
"B = math.ceil(B*10**3)/10**3; #rounding off the value of B to 3 decimals\n",
"mew_r = M/H + 1; #The relative permeability of diamagnetic material\n",
"mew_r = math.ceil(mew_r*10**6)/10**6; #rounding off the value of mew_r to 6 decimals\n",
"\n",
"#Result\n",
"print \"The magnetisation of diamagnetic material is\",M, \"A/m\"\n",
"print \"The magnetic flux density of diamagnetic material is\",B, \"T\"\n",
"print \"The relative permeability of diamagnetic material is\",mew_r\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetisation of diamagnetic material is -0.504 A/m\n",
"The magnetic flux density of diamagnetic material is 0.151 T\n",
"The relative permeability of diamagnetic material is 0.999996\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.6, Page number 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"chi = 5.6*10**-6; #Magnetic susceptibility of diamagnetic material\n",
"m = 9.1*10**-31; #Mass of an electron(kg)\n",
"mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n",
"Z = 1; #Atomic number\n",
"e = 1.6*10**-19; #Electronic charge(C)\n",
"a = 2.53; #Lattice parameter of bcc structure(A)\n",
"\n",
"#Calculation\n",
"a = a*10**-10; #Lattice parameter of bcc structure(m)\n",
"N = 2/a**3; #The number of electrons per unit volume(per metre cube)\n",
"r = math.sqrt(chi*6*m/(mew_0*Z*e**2*N)); #Mean radius of body centered cubic structure(m)\n",
"r = r*10**10; #Mean radius of body centered cubic structure(A)\n",
"r = math.ceil(r*100)/100; #rounding off the value of r to 2 decimals\n",
"\n",
"#Result\n",
"print \"The mean radius of body centered cubic structure is\",r, \"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mean radius of body centered cubic structure is 0.88 A\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 14.7, Page number 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n",
"N_A = 6.02*10**26; #Avogadro's number(per kmol)\n",
"rho = 4370; #Density of paramegnetic salt(kg/metre cube)\n",
"M = 168.5; #Molecular weight of paramagnetic salt(g/mol)\n",
"T = 27; #Temperature of paramagnetic salt(C)\n",
"H = 2*10**5; #Field strength to which the paramagnetic salt is subjected(A/m)\n",
"mew_B = 9.27*10**-24; #Bohr's magneton(Am**2)\n",
"p = 2; #Number of Bohr magnetons per molecule\n",
"k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
"\n",
"#Calculation\n",
"T = T+273; #Temperature of paramagnetic salt(K)\n",
"N = rho*N_A/M; #Total density of atoms in the paramagnetic salt(per meter cube)\n",
"chi_para = mew_0*N*p**2*mew_B**2/(3*k*T); #Magnetic susceptibility of paramagnetic salt\n",
"chi_para = chi_para*10**4;\n",
"chi_para = math.ceil(chi_para*10**2)/10**2; #rounding off the value of chi_para to 2 decimals\n",
"M = chi*H; #Magnetisation of paramagnetic salt(A/m)\n",
"M = math.ceil(M*10)/10; #rounding off the value of M to 1 decimal\n",
"\n",
"#Result\n",
"print \"The magnetic susceptibility of paramagnetic salt is\",chi_para,\"*10**-4\"\n",
"print \"The magnetisation of paramagnetic salt is\",M, \"A/m\"\n",
"\n",
"#answer for magnetisation is not given in the textbook"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetic susceptibility of paramagnetic salt is 5.43 *10**-4\n",
"The magnetisation of paramagnetic salt is 1.2 A/m\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}