{
"metadata": {
"celltoolbar": "Raw Cell Format",
"name": "",
"signature": "sha256:bc506d3130781232c57938d478c5c5179ee56efb068c1be93d57258ec96fcd79"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: Magnetic Materials and Circuits"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1,Page number 2-26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"H=198 #Magnetizing Force in Ampere per meter\n",
"M=2300 #Magnetization in Ampere per meter\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"\n",
"#Calculations:\n",
"#H=(B/u0)-M\n",
"B=u0*(H+M) #Flux Density\n",
"ur=B/(u0*H) #Relative Permeability\n",
"\n",
"print\"Corresponding Flux Density is =\",B,\"Wb/m^2\"\n",
"print\"Relative Permeability is =\",ur\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Corresponding Flux Density is = 0.00313907937947 Wb/m^2\n",
"Relative Permeability is = 12.6161616162\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2,Page number 2-26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"x=3.7*10**-3 #Susceptibility at T=300 K\n",
"T=300 #Temperature in kelvin\n",
"T1=250 #Temperature in kelvin\n",
"T2=600 #Temperature in kelvin\n",
"\n",
"#Calculations:\n",
"C=x*T #Curie's law\n",
"ur1=C/T1 #Relative permeability at 250 K\n",
"ur2=C/T2 #Relative permeability at 600 K\n",
"\n",
"print\"Relative Permeability at 250 K is =\",ur1\n",
"print\"Relative Permeability at 600 K is =\",ur2\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Relative Permeability at 250 K is = 0.00444\n",
"Relative Permeability at 600 K is = 0.00185\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3,Page number 2-27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u=0.8*10**-23 #Magnetic dipole moment of an atom in paramagnetic gas in J/T\n",
"B=0.8 #Magnetic field in tesla\n",
"K=1.38*10**-23 #Boltzmann constant\n",
"\n",
"#To find Temperature at which Average thermal energy is equal to Magnetic energy \n",
"#i.e. uB=3KT/2\n",
"T=2*u*B/(3*K) #Required temperature\n",
"\n",
"print\"Required temperature is =\",T,\"Kelvin\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Required temperature is = 0.309178743961 Kelvin\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4,Page number 2-27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"T=27+273 #Temperature in kelvin\n",
"B=0.5 #Magnetic field in tesla\n",
"C=2*10**-3 #Curie's Constant\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"\n",
"# C=u0*M*T/B (Curie's law)\n",
"M=C*B/(u0*T) #Magnetization of material at 300 K\n",
"\n",
"print\"Magnetization of material at 300 K is =\",M,\"A/m\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetization of material at 300 K is = 2.65258238486 A/m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5,Page number 2-27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"B=10.9*10**-5 #Horizontal component of B in wb/m^2\n",
"u0=4*math.pi*10**-7 #Permeability in free space\n",
"\n",
"H=B/u0 #Horizontal component of magnetic field\n",
"print\"Horizontal component of magnetic field is =\",H,\"Ampere/meter\"\n",
"print\"(Print mistake in unit in book)\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Horizontal component of magnetic field is = 86.7394439851 Ampere/meter\n",
"(Print mistake in unit in book)\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6,Page number 2-28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=900 #Relative permeability of medium\n",
"l=2 #length in meter\n",
"A=60*10**-4 #Crosss sectional area of ring in m^2\n",
"phi=5.9*10**-3 #flux in weber\n",
"n=700 #Number of turns\n",
"\n",
"#Calculations:\n",
"#We know, phi=B*A\n",
"B=phi/A #Flux density\n",
"#But, B=u*H\n",
"H=B/(u0*ur) #Magnetic field strength\n",
"\n",
"I=H*l/n #Required current\n",
"print\"Current required to produce given flux is =\",I,\"Ampere\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current required to produce given flux is = 2.48416445567 Ampere\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7,Page number 2-28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=900 #Relative permeability of medium\n",
"r=25*10**-2 #radius of ring\n",
"A=25*10**-4 #Crosss sectional area of ring in m^2\n",
"Ag=1*10**-3 #Air gap\n",
"phi=2.7*10**-3 #flux in weber\n",
"N=400 #Number of turns\n",
"\n",
"#Calculations:\n",
"#We know, phi=B*A\n",
"B=phi/A #Flux density\n",
"#But, B=u*H\n",
"H=B/(u0*ur) #Magnetic field strength\n",
"L=H*2*math.pi*r+(B*Ag/u0) #Total amp turns required (iron+air)\n",
"I=L/N #Required current\n",
"\n",
"print\"Current required to produce given flux is =\",I,\"Ampere\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current required to produce given flux is = 5.89859173174 Ampere\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.8,Page number 2-29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"A=0.2*10**-4 #Crosss sectional area of iron bar in m^2\n",
"H=1600 #magnetising field in A/m\n",
"phi=2.4*10**-5 #Magnetic flux in weber\n",
"\n",
"\n",
"#Calculations:\n",
"#We know, phi=B*A\n",
"B=phi/A #Flux density\n",
"u=B/H #magnetic permeability\n",
"ur=u/u0 #relative permeability\n",
"xm=ur-1 #susceptibility of the iron bar\n",
"\n",
"print\"magnetic permeability of iron bar is =\",u,\"N/(A^2)\"\n",
"print\"susceptibility of the iron bar is =\",xm\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"magnetic permeability of iron bar is = 0.00075 N/(A^2)\n",
"susceptibility of the iron bar is = 595.831036595\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.9,Page number 2-29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"xm=948*10**-11 #susceptibility of the iron bar\n",
"\n",
"#Calculations:\n",
"ur=1+xm #relative permeability\n",
"u=u0*ur #permeability of medium\n",
"\n",
"print\"Relative Permeability of medium is =\",ur\n",
"print\"Permeability of medium is =\",u,\"H/m\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Relative Permeability of medium is = 1.00000000948\n",
"Permeability of medium is = 1.25663707335e-06 H/m\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.10,Page number 2-30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"B=2.5 #Magnetic field in tesla\n",
"u0=4*math.pi*10**-7 #Permeability in free space\n",
"i0=0.7 #current in the core\n",
"ri=11*10**-2 #inner radii of core\n",
"ro=12*10**-2 #outer radii of core\n",
"\n",
"#Calculations:\n",
"r=(ri+ro)/2 #Average radii of core\n",
"n=3000/(2*math.pi*r) #Number of turns\n",
"\n",
"#We know, B=u0*ur*n*i0 .Thus,\n",
"ur=B/(u0*n*i0)\n",
"\n",
"print\"Relative Permeability of medium is =\",ur\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Relative Permeability of medium is = 684.523809524\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.11,Page number 2-31"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"B=1.0 #Flux density in tesla\n",
"u0=4*math.pi*10**-7 #Permeability in free space\n",
"i=2.0 #current in the core\n",
"n=10*100 #n=N/l i.e. turns per meter\n",
"\n",
"#Calculations:\n",
"H=n*i #Magnetising force produced in wire\n",
"print\"Magnetising force produced in wire is =\",H,\"Amp-turn/meter\"\n",
"\n",
"#We know that, B=u0(H+I).Thus,\n",
"I=B/u0-H #Magnetisation of material\n",
"print\"Magnetisation of material is =\",I,\"Amp-turn/meter\"\n",
"\n",
"#u=B/H, i.e. ur*u0=B/H.\n",
"ur=B/(u0*H) #Relative permeability of core\n",
"print\" Relative Permeability of core is =\",ur\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetising force produced in wire is = 2000.0 Amp-turn/meter\n",
"Magnetisation of material is = 793774.715459 Amp-turn/meter\n",
" Relative Permeability of core is = 397.88735773\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.12,Page number 2-31"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"M=40 #Mass of an iron core\n",
"D=7.5*10**3 #Density of iron\n",
"f=100 #Frequency\n",
"A=3800*10**-1 #Loss due to Area of hysterisis loop in J/m^3\n",
"\n",
"#Calculations:\n",
"V=M/D #Volume of iron core\n",
"L1=A*V #Loss of energy in core per cycle\n",
"print\"Loss of energy in core per cycles is =\",L1,\"joules\"\n",
"\n",
"N=f*60 #Number of cycles per minute\n",
"L=L1*N #Loss of energy per minute\n",
"\n",
"print\"Loss of energy per minute is =\",L,\"joules\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Loss of energy in core per cycles is = 2.02666666667 joules\n",
"Loss of energy per minute is = 12160.0 joules\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.13,Page number 2-32"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"l=30*10**-2 #length in meter\n",
"A=1*10**-4 #Crosss sectional area of ring in m^2\n",
"phi=2*10**-6 #flux in weber\n",
"N=300 #Number of turns\n",
"I=0.032 #Current in winding\n",
"\n",
"#Calculations:\n",
"#(i):\n",
"B=phi/A #Flux density\n",
"print\"(i)Flux Density in the ring is =\",B,\"Wb/m^2\"\n",
"\n",
"#(ii):\n",
"H=N*I/l #Magnetic intensity\n",
"print\"(ii)Magnetic intensity is =\",H,\"Amp-turn/meter\"\n",
"\n",
"#(iii):\n",
"u=B/H #Permeability of ring\n",
"print\"(iii)Permeability of ring is =\",u,\" Wb/A-m\"\n",
"ur=u/u0 #Relative permeability of ring\n",
"print\"Relative Permeability of ring is =\",ur\n",
"\n",
"#(iv):\n",
"xm=ur-1 #susceptibility of the ring\n",
"print\"(iv)Magnetic susceptibility of the ring is =\",xm\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i)Flux Density in the ring is = 0.02 Wb/m^2\n",
"(ii)Magnetic intensity is = 32.0 Amp-turn/meter\n",
"(iii)Permeability of ring is = 0.000625 Wb/A-m\n",
"Relative Permeability of ring is = 497.359197162\n",
"(iv)Magnetic susceptibility of the ring is = 496.359197162\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.14,Page number 2-32"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Dta:\n",
"M=12*10**3 #Mass of an iron core in grams\n",
"D=7.5 #Density of iron in gm/cc\n",
"f=50 #Frequency\n",
"A=3000 #loss due to Area of hysterisis loop in ergs/cm^3\n",
"\n",
"#Calculations:\n",
"V=M/D #Volume of iron core\n",
"L1=A*V #Loss of energy in core per cycle\n",
"\n",
"L=L1*f*3600 #Loss of energy per hour\n",
"\n",
"print\"Loss of energy per hour is =\",L,\"Erg\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Loss of energy per hour is = 8.64e+11 Erg\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.15,Page number 2-33"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"A=0.5*10**3 #Area of B-H loop in Joules per m^3\n",
"V=10**-3 #Volume of specimen in m^3\n",
"n=50 #Frequency of a.c.\n",
"\n",
"#Calculations:\n",
"H=n*V*A #Hysteresis power loss\n",
"\n",
"print\"Hysteresis power loss is =\",H,\"Watt\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hysteresis power loss is = 25.0 Watt\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.16,Page number 2-33"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=1000 #Relative permeability of medium\n",
"V=10**-4 #Volume of iron rod in m^3\n",
"n=500 #Number of turns per meter\n",
"i=0.5 #Current in windings of solenoid in Amperes\n",
"\n",
"#Calculations:\n",
"#We know I=(ur-1)H\n",
"#and H=ni , hence\n",
"I=(ur-1)*n*i #Intensity of magnetisation\n",
"M=I*V #Magnetic moment\n",
"\n",
"print\"Magnetic moment of the rod is =\",M,\"A-m^2\"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic moment of the rod is = 24.975 A-m^2\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.17,Page number 2-34"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=600 #Relative permeability of iron\n",
"d=12*10**-2 #mean diameter of ring in m\n",
"N=500 #Number of turns\n",
"i=0.3 #Current in windings of solenoid in Amperes\n",
"\n",
"#Calculations:\n",
"r=d/2 #Radius of ring\n",
"\n",
"B=u0*ur*N*i/(2*math.pi*r) #Flux densityin the core\n",
"print\"Flux densityin the core is =\",B,\"Wb/m^2\"\n",
"\n",
"H=B/(u0*ur) #Magnetic intensity\n",
"print\"Magnetic intensity is =\",H,\"Amp-turns/m\"\n",
"\n",
"#We know that, B=u0(H+I)\n",
"I1=(B-u0*H)/u0 #magnetisation\n",
"I2=u0*I1 #Electronic current loop\n",
"\n",
"I=I2/B*100 #Percentage flux density due to electroniuc loop currents\n",
"print\"Percentage flux density due to electroniuc loop currents is =\",I,\"percent\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flux densityin the core is = 0.3 Wb/m^2\n",
"Magnetic intensity is = 397.88735773 Amp-turns/m\n",
"Percentage flux density due to electroniuc loop currents is = 99.8333333333 percent\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.18,Page number 2-35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=900 #Relative permeability of iron ring\n",
"d=40*10**-2 #diameter of ring\n",
"l=5*10**-3 #air gap in the ring\n",
"A=5.8*10**-4 #Crosss sectional area of ring in m^2\n",
"phi=1.5*10**-4 #flux in weber\n",
"N=600 #Number of turns\n",
"\n",
"#Calculations:\n",
"r=d/2 #Radius of ring\n",
"\n",
"#We know, phi=B*A\n",
"B=phi/A #Flux density\n",
"\n",
"#But, B=u*H\n",
"H=B/(u0*ur) #Magnetic field strength\n",
"\n",
"m1=H*ur*l #amp-turns in air gap\n",
"m2=H*2*math.pi*r #amp-turns by ring\n",
"m=m1+m2 #total mmf(amp-turns) required\n",
"\n",
"I=m/N #Required current\n",
"print\"Current required to produce given flux is =\",I,\"Amperes\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current required to produce given flux is = 2.19395891742 Amperes\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.18.1,Page number 2-38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"X=-0.5*10**-5 #Magnetic susceptibility of silicon\n",
"H=9.9*10**4 #Magnetic field intensity\n",
"\n",
"#Calculations:\n",
"\n",
"#As, X=I/H. thus,\n",
"I=X*H #intensity of magnetisation\n",
"print\"Intensity of magnetisation is =\",I\n",
"\n",
"B=u0*(H+I) #Magnetic flux density\n",
"print\"Magnetic flux density is =\",B,\"Wb/ m^2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Intensity of magnetisation is = -0.495\n",
"Magnetic flux density is = 0.124406447047 Wb/ m^2\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.18.2,Page number 2-38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=380 #Relative permeability\n",
"d=20*10**-2 #diameter of solenoid in m\n",
"r=d/2 #radius of ring in m\n",
"A=5*10**-4 #Crosss sectional area of ring in m^2\n",
"phi=2*10**-3 #flux in weber\n",
"N=200 #Number of turns\n",
"\n",
"#Calculations:\n",
"l=math.pi*d #air gap in the ring\n",
"S=(l/(u0*ur*A)) #Reluctance of iron ring\n",
"print\"Reluctance of iron ring is =\",S,\"Amp-turn/ Wb \"\n",
"\n",
"#ohm's law for magnetic circuit is phi=N*I/S. thus,\n",
"I=S*phi/N #required current\n",
"print\"Current required to obtain given magnetic flux is =\",I,\"Amperes\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Reluctance of iron ring is = 2631578.94737 Amp-turn/ Wb \n",
"Current required to obtain given magnetic flux is = 26.3157894737 Amperes\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.18.3,Page number 2-39"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Values:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=1 #Relative permeability of air\n",
"r=15*10**-2 #radius of ring in m\n",
"A=6*10**-4 #Crosss sectional area of ring in m^2\n",
"I=4 #Coil current in amp\n",
"N=500 #Number of turns\n",
"\n",
"#Calculations:\n",
"m=N*I #MMF of coil\n",
"print\"MMF of coil is =\",m,\"Ampere-turn\"\n",
"\n",
"l=2*math.pi*r #air gap\n",
"R=(l/(u0*ur*A)) #Reluctance of iron ring\n",
"print\"Reluctance of iron ring is =\",R,\"Ampere-turn/Wb\"\n",
"\n",
"phi=m/R #Magnetic flux\n",
"print\"Magnetic flux is =\",phi,\"Weber\"\n",
"\n",
"B=phi/A #Magnetic Flux density\n",
"print\"Magnetic flux density is =\",B,\"Weber/m^2\"\n",
"\n",
"H=B/(u0*ur) #Magnetic field intensity\n",
"print\"Magnetic field intensity is =\",H,\"Amperes/m\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"MMF of coil is = 2000 Ampere-turn\n",
"Reluctance of iron ring is = 1250000000.0 Ampere-turn/Wb\n",
"Magnetic flux is = 1.6e-06 Weber\n",
"Magnetic flux density is = 0.00266666666667 Weber/m^2\n",
"Magnetic field intensity is = 2122.06590789 Amperes/m\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.19,Page number 2-36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"u0=4*math.pi*10**-7 #Permeability in vacuum\n",
"ur=6*10**-3 #Relative permeability of iron\n",
"r=0.5 #radius of ring in m\n",
"l=1*10**-2 #air gap in the ring\n",
"A=5*10**-4 #Crosss sectional area of ring in m^2\n",
"i=5 #current in ampere\n",
"N=900 #Number of turns\n",
"\n",
"#Calculations:\n",
"S=(l/(u0*A))+((2*math.pi*r-l)/ur*A) #Reluctance of iron\n",
"print\"Reluctance of iron is =\",S,\"Ampere-turn/Wb\"\n",
"\n",
"m=N*i #mmf produced\n",
"print\"mmf produced is =\",m,\"Ampere-turn\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Reluctance of iron is = 15915494.5702 Ampere-turn/Wb\n",
"mmf produced is = 4500 Ampere-turn\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.20,Page number 2-36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"H=5*10**3 #coercivity of bar magnet in amp/m\n",
"l=10*10**-2 #length of solenoid in m\n",
"N=50 #No of turns\n",
"\n",
"#Calculations:\n",
"\n",
"#We know that, H=NI/l ,hence\n",
"I=l*H/N #current through solenoid\n",
"\n",
"print\"Current through solenoid is =\",I,\"Amperes\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current through solenoid is = 10.0 Amperes\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.21,Page number 2-36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"ur=1200 #Relative permeability of medium\n",
"V=10**-3 #volume of iron rod\n",
"N=5*10**2 #no of turns per m\n",
"i=0.5 #current through solenoid in amp\n",
"\n",
"#Calculations:\n",
"x=ur-1 #susceptibility of the ring\n",
"H=N*i #Magnetisisng field\n",
"\n",
"#We know, x=I/H\n",
"I=x*H #magnetisation\n",
"\n",
"#Also, I=M/V , thus\n",
"M=I*V #magnetic moment\n",
"print\"Magnetic moment is =\",M,\"Ampere-turn-m^2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic moment is = 299.75 Ampere-turn-m^2\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.22,Page number 2-37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Dta:\n",
"ur=100 #Relative permeability of medium\n",
"l=0.2 #length of iron rod\n",
"d=10*10**-3 #diameter of solenoid in m\n",
"N=300 #no of turns per m\n",
"i=0.5 #current through solenoid in amp\n",
"r=d/2 #radius of solenoid\n",
"\n",
"#Calculations:\n",
"x=ur-1 #susceptibility of the ring\n",
"H=N*i #Magnetisisng field\n",
"\n",
"#We know, x=I/H\n",
"I=x*H #magnetisation\n",
"\n",
"V=math.pi*(r**2)*l #volume of iron rod\n",
"\n",
"#Also, I=M/V , thus\n",
"M=I*V #magnetic moment\n",
"print\"Magnetic moment is =\",M,\"Ampere-turn-m^2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnetic moment is = 0.233263254529 Ampere-turn-m^2\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.23,Page number 2-38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given Data:\n",
"l=1.2 #length of circuit in meter\n",
"u=7.3*10**-3 #permeability of silicon sheet\n",
"A=100 #cross sectional area in cm^2\n",
"N=150 #No of turns\n",
"B=0.3 #magmetic field in Wb/m^2\n",
"\n",
"#Calculations:\n",
"\n",
"#We know, B=u*H\n",
"H=B/u #Magnetic field strength\n",
"\n",
"m=H*l #amp-turns in air gap\n",
"\n",
"I1=m/N #Required current\n",
"print\"Current required to obtain given magnetic field is =\",I1,\"Amperes\"\n",
"\n",
"I=I1/A #Required current per unit area\n",
"print\"Current required per unit area to obtain given magnetic field is =\",I,\"Amperes\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Current required to obtain given magnetic field is = 0.328767123288 Amperes\n",
"Current required per unit area to obtain given magnetic field is = 0.00328767123288 Amperes\n"
]
}
],
"prompt_number": 34
}
],
"metadata": {}
}
]
}