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{
"metadata": {
"name": "",
"signature": "sha256:3eb552fb3c1a7764bbfbba83330f0d6a18ee201068631d5f4e4579961984a5eb"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter4:MAGNETIC PROPERTIES OF MATERIALS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg1:pg-153"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"phi_B=2.4e-5 #magnetic flux in weber\n",
"A=0.2 #cross-sectional area in cm**2\n",
"H=1600 #magnetising field in A/m\n",
"mu_o=4*round(math.pi,2)*1e-7 #absolute permeability of air in N/A**2\n",
"B=phi_B/(A*1e-4)\n",
"mu=B/H\n",
"Xm=mu/mu_o-1\n",
"print\"Magnetic permeability of iron bar is \",\"{:.1e}\".format(mu),\"N/A**2\"\n",
"print\"Magnetic susceptibility of iron bar is \",round(Xm,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic permeability of iron bar is 7.5e-04 N/A**2\n",
"Magnetic susceptibility of iron bar is 596.13\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg2:pg-154"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import *\n",
"Xm=948e-11 #magnetic susceptibility of a medium\n",
"pi=Symbol('pi')\n",
"mu_o=4*pi*1e-7 #absolute permeability of air in H/m\n",
"mu_r=1+Xm\n",
"mu=int(mu_r)*mu_o\n",
"print\"Relative Permeability is =\",mu_r,\"=\",int(mu_r),\"or >\",int(mu_r)\n",
"print\" Relative permeability is slightly greater than one.\"\n",
"print\"Permeability is =\",mu,\"H/m\" #answer in book is 4*(pi)*1e-7 H/m"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Relative Permeability is = 1.00000000948 = 1 or > 1\n",
" Relative permeability is slightly greater than one.\n",
"Permeability is = 4.0e-7*pi H/m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg3:pg-154"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mu_r=1200 #relative permeability of iron rod\n",
"n=5 #number of turns per cm\n",
"i=0.5 #current in ampere\n",
"V=1e-3 #volume of iron rod in m**3\n",
"I=(mu_r-1)*(n*1e2)*i\n",
"M=I*V\n",
"print\"Magnetic moment is \",\"{:.0e}\".format(M),\"Am**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic moment is 3e+02 Am**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg4:pg-155"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"mu_r=100 #relative permeability of iron rod\n",
"n=300 #number of turns per meter\n",
"i=0.5 #current in ampere\n",
"D=10 #diameter of iron rod in mm\n",
"r=D/2 #radius of iron rod in mm\n",
"l=2 #length of iron rod in meter\n",
"I=(mu_r-1)*n*i\n",
"V=round(math.pi,2)*(r*1e-3)**2*l\n",
"M=I*V\n",
"print\"Magnetic moment is \",round(M,3),\"Am**2\"\n",
"#answer in book is wrong as the value of l is taken wrong in calcultion. "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic moment is 2.331 Am**2\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg5:pg-163"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"n=1e29 #number of atoms per unit volume in atoms/m**3\n",
"Pm=1.8e-23 #magnetic moment of one atom in A-m**2\n",
"K=1.38e-23 #Boltzmann's constant in J/K\n",
"T=300 #temperature in Kelvin\n",
"mu_o=4*round(math.pi,2)*10**-7 #absolute permeability of air in N/A**2\n",
"B=0.1 #magnetic flux density in weber/m**2\n",
"A=1 #cross-section area in cm**2\n",
"l=10 #length of iron bar in cm\n",
"Xm=mu_o*n*Pm**2/(3*K*T) #magnetic susceptibility of iron bar\n",
"P_m=Pm**2*B/(3*K*T) #mean dipole moment of an iron atom in A-m**2\n",
"V=(A*1e-4)*(l*1e-2) #volume of iron bar in m**3\n",
"n_o_a=V*n \n",
"dm=n_o_a*P_m #dipole moment of the iron bar \n",
"I=Pm*n \n",
"m=I*V\n",
"print\"Magnetic Susceptibility is \",\"{:.3e}\".format(Xm)\n",
"print\"Dipole moment is \",\"{:.3e}\".format(dm),\"Am**2\"\n",
"print\"Magnetisation is \",\"{:.1e}\".format(I),\"A/m\"\n",
"print\"Magnetic moment is \",int(m),\"Am**2\"#this answer is wrong in book"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic Susceptibility is 3.277e-03\n",
"Dipole moment is 2.609e-03 Am**2\n",
"Magnetisation is 1.8e+06 A/m\n",
"Magnetic moment is 18 Am**2\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6:pg-169"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"H=5e3 #Coercivity of bar magnet in ampere/m \n",
"l=10 #length of solenoid in cm\n",
"n=50 #number of turns in solenoid\n",
"i=H*(l*1e-2)/n\n",
"print\"Current is \",int(i),\"amp\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current is 10 amp\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg8:pg-170"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a=250 #area of B-H loop in J/m**3\n",
"f=50 #frequency of a.c. in Hz\n",
"m=9.0 #mass of iron core in Kg\n",
"p=7500 #density of iron in Kg/m**3\n",
"V=m/p\n",
"n=50*60*60\n",
"E=n*V*a\n",
"print\"Hysteresis loss of energy E per hour is \",\"{:.1e}\".format(E),\"J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hysteresis loss of energy E per hour is 5.4e+04 J\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg10:pg-170"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"A=0.785e-4 #cross-sectional area of rowland ring in m**2\n",
"Ri=5.0 #inner radius in cm\n",
"Ro=6.0 #outer radius in cm\n",
"N=400 #number of turns of wire\n",
"Bo=2e-4 #magnetic flux density in weber/m**2\n",
"mu_o=4*math.pi*10**-7 #absolute permeability of air in N/A**2\n",
"Ns=50 #number of turns in secondary coil\n",
"R=8.0 #resistance in ohm\n",
"B1=800*Bo #magnetic flux density in weber/m**2\n",
"l=2*math.pi*(Ri+Ro)*1e-2/2\n",
"i=Bo*l/(mu_o*N)\n",
"q=Ns*B1*A/R\n",
"print\"Required Current is \",i,\"amp\"\n",
"print\"Charge passed is \",q,\"coulomb\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Required Current is 0.1375 amp\n",
"Charge passed is 7.85e-05 coulomb\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg11:pg-171"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"mu_r=400 #relative permeability of iron ring\n",
"r=0.1 #mean radius of iron ring in meter\n",
"A=5e-4 #cross-sectional area of iron ring in m**2\n",
"n=1000 #number of turns of wire\n",
"i=4 #current in ampere\n",
"mu_o=4*math.pi*10**-7 #absolute permeability of air in N/A**2\n",
"B=mu_o*mu_r*n*i/(2*math.pi*r)\n",
"phi=B*A \n",
"print\"Flux in the ring is \",\"{:.2e}\".format(phi),\"weber\"\n",
"n_o=500 #number of turns in secondary coil per meter\n",
"R=10 #resistance in ohm\n",
"q=2*n_o*A*B/R\n",
"print\"Electricity discharged through the secondary coil is \",q,\"coulomb\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flux in the ring is 1.60e-03 weber\n",
"Electricity discharged through the secondary coil is 0.16 coulomb\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg12:pg-171"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m=12 #weight of the iron core in Kg\n",
"p=7.5 #density of iron core in gm/cc\n",
"f=50 #frequency in cycles/sec\n",
"a=3000 #area of hysteresis loop in ergs/cm**3 (unit is misprinted in question in book)\n",
"V=(m*1e3)/p\n",
"n=f*60*60\n",
"E=n*V*a\n",
"print\"Hourly loss of energy is \",E,\"erg\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hourly loss of energy is 8.64e+11 erg\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg13:pg-172"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a=0.5 #area of B-H loop in cm**2\n",
"H=1e3 #value of 1 cm on X-axis in A/m\n",
"B=1 #value of 1 cm on Y-axis in Tesla\n",
"V=1e-3 #volume of specimen in m**3\n",
"n=50 #frequency of a.c. in Hz\n",
"area=a*H*B #area of B-H loop in J/m**3 (this is misprinted in solution in book)\n",
"p=n*V*area\n",
"print\"Hysteresis power loss is \",int(p),\"Watt\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hysteresis power loss is 25 Watt\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
