{
"metadata": {
"name": "",
"signature": "sha256:354118d2fca7350165cb8c5d000bd36293e8da69f0cbb274034a02640d69b2e6"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 4: Magnetic Fields and Circuits"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.1, Page 116"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"A = 6e-04; # Cross-sectional area of pole face, metre-square\n",
"phi = 30e-06; # Flux, Wb\n",
"\n",
"#Calculations\n",
"B = phi/A; # Flux density, T\n",
"\n",
"#Result\n",
"print \"The flux density at the pole face = %2d mT\"%(B/1e-03)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The flux density at the pole face = 50 mT\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.2, Page 116"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"A = 45e-06; # Cross sectional area of pole face, metre-square\n",
"B = 0.6; # Flux density, T\n",
"\n",
"#Calculations\n",
"# Using formula B = phi/A, solving for phi\n",
"phi = B*A; # Flux, Wb\n",
"\n",
"#Result\n",
"print \"The flux produced by pole face = %2d micro-wWb\"%(phi/1e-06);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The flux produced by pole face = 27 micro-wWb\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.3, Page 117"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"N = 1500; # Number of turns in a coil\n",
"A = 5e-04; # Cross- sectional area of of coil, metre-square\n",
"phi = 0.2e-03; # Flux, Wb\n",
"I = 0.75; # Coil-current, A\n",
"\n",
"#Calculations\n",
"# Since m.m.f is the product of the current and the number of turns, therefore, we have\n",
"F = N*I; # Magnetomotive force, At\n",
"B = phi/A; # Flux density, T\n",
"\n",
"#Result\n",
"print \"The m.m.f and flux density produced are %4d At and %3.1f T respectively\"%(F, B);\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The m.m.f and flux density produced are 1125 At and 0.4 T respectively\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4, Page 117"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"N = 600; # Number of turns in a coil\n",
"F = 1500.; # Magnetomotive force, At\n",
"\n",
"#Calculations\n",
"# Since magnetomotive force,F = N*I, solving for I\n",
"I = F/N; # Excitation-current, A\n",
"\n",
"#Result\n",
"print \"The excitation current required = %3.1f A\"%I;\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The excitation current required = 2.5 A\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.5, Page 118"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"I = 0.4; # Current, A\n",
"N = 550; # Number of turns in a coil\n",
"d = 8e-02; # Diameter, m\n",
"l = (math.pi*d); # Average length of the magnetic circuit, m\n",
"\n",
"#Calculations\n",
"# Since magnetic field strength is defined as the mmf per metre length of the magnetic circuit, therefore, we have\n",
"H = (N*I)/l; # Magnetic field strength, At/m\n",
"\n",
"#Result\n",
"print \"The magnetic field strength inside the toroid = %6.2f At/m\"%H\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetic field strength inside the toroid = 875.35 At/m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.6, Page 120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"A = 15e-04; # Cross-sectional area of core, metre-square\n",
"mew_r1 = 65; # Relative permeability of core\n",
"phi_1 = 2e-04; # Flux, Wb\n",
"mew_r2 = 800.; # Changed relative permeability of core\n",
"\n",
"#Calculations\n",
"B_1 = phi_1/A; # Flux density, T\n",
"mew_r = mew_r2/mew_r1; # Relative permeability of core\n",
"# Since cross-sectional area of core A remains constant, therefore, we have mew_r = B_1/B_2 , solving for B_2\n",
"B_2 = mew_r*B_1; # New flux density, T\n",
"# Since B_2 = phi_2/A, solving for phi_2\n",
"phi_2 = B_2*A; # New flux, Wb\n",
"\n",
"#Result\n",
"print \"The new flux and flux density are %5.3f mWb and %5.3f T respectively\"%(phi_2/1e-03, B_2);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The new flux and flux density are 2.462 mWb and 1.641 T respectively\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.7, Page 120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"r = 0.04; # Mean radius of torod, m\n",
"A = 3e-04; # Csa of toroid, m^2\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability of free space\n",
"mew_r = 150; # Relative permeability of toroid\n",
"N = 900; # Number of turns on coil\n",
"I = 1.5; # Coil current, A\n",
"l = 2*(math.pi)*r; # Effective length of toroid, m\n",
"\n",
"#Calculations&Results\n",
"# Part (a)\n",
"# Since m.m.f is the product of the current and the number of turns, therefore, we have\n",
"F = N*I; # Magnetomotive force, At\n",
"print \"The m.m.f of toroid = %4d At\"%F\n",
"\n",
"# Part (b)\n",
"# Since magnetic field strength is defined as the mmf per metre length of the magnetic circuit, therefore, we have\n",
"H = F/l; # Magnetic field strength, At/m\n",
"print \"The magnetic field strength = %6.1f At/m\"%H;\n",
"\n",
"# Part (c)\n",
"B = (mew_r*mew_o*H); # Flux density, T\n",
"phi = B*A; # Flux, Wb\n",
"print \"The flux and flux density are %6.2f micro-weber and %6.4f T respectively\"%(phi/1e-06,B)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The m.m.f of toroid = 1350 At\n",
"The magnetic field strength = 5371.5 At/m\n",
"The flux and flux density are 303.75 micro-weber and 1.0125 T respectively\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.8, Page 120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"r = 3e-02; # Radius of toroid, m\n",
"A = 4.5e-04; # Cross-sectional area of toroid, metre-square\n",
"N = 500; # Number of turns \n",
"phi = 250e-06; # Flux, Wb\n",
"mew_o = 4*(math.pi)*(1e-07); # Permeability of free space\n",
"mew_r = 300; # Relative permeability\n",
"\n",
"#Calculations\n",
"l = 2*(math.pi)*r; # Effective length, m\n",
"B = phi/A; # Flux density, T\n",
"# Since B = (mew_r)*(mew_o)*H, solving for H\n",
"H = B /((mew_r)*(mew_o)); # Magnetic field strength, At/m\n",
"# Since H = F/l, solving for F\n",
"F = H*l; # Magnetomotive force, At\n",
"# Since mmf,F = N*I, solving for I\n",
"I = F/N; # Electric current, A\n",
"\n",
"#Result\n",
"print \"The value of current needs to be passed through the coil = %4.2f A\"%I\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of current needs to be passed through the coil = 0.56 A\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.9, Page 121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"# Part (a)\n",
"I = 0.2; # Electric current, A\n",
"l = 5e-02; # Effective length, m\n",
"A = 7e-04; # Cross-sectional area, metre-square\n",
"d = 0.5e-03; # Diameter, m\n",
"mew_r = 1; #Relative permeability for wood\n",
"\n",
"#Calculations\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability for free space\n",
"N = l/d; # Number of turns \n",
"# Since mmf is the product of the current and the number of turns, therefore, we have\n",
"F = N*I; # Magnetomotive force, At\n",
"# Part (b)\n",
"# Since magnetic field strength is defined as the mmf per metre length of the magnetic circuit, therefore, we have\n",
"H = F/l; # Magnetic field strength, At/m\n",
"B = ( mew_r * mew_o * H ); # Flux density, T\n",
"# Part (c)\n",
"phi = B * A; # Flux, Wb\n",
"\n",
"#Result\n",
"print \"The mmf produced = %2d At\"%F\n",
"print \"The flux density produced = %3d micro-tesla\"%(B/1e-06);\n",
"print \"The flux produced = %5.3f micro-weber\"%(phi/1e-06);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mmf produced = 20 At\n",
"The flux density produced = 502 micro-tesla\n",
"The flux produced = 0.352 micro-weber\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.10, Page 125"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"N = 1000; # Number of turns on coil\n",
"r = 0.1; # Mean radius of toroid, m\n",
"phi = 0.1775e-03; # Flux density(value from graph), Wb\n",
"A = math.pi*1e-04; # Csa of toroid, m^2\n",
"H = 88; # Magnetic field strength(value from graph), At/m\n",
"B = phi/A; # Flux density, T\n",
"\n",
"#Calculations&Results\n",
"# Part (a)\n",
"l = 2*math.pi*r; # Effective length of toroid, m\n",
"# Since H = (N*I)/l, solving for I\n",
"I = (H*l)/N ; # Electric current in coil, A\n",
"print \"Coil current = %4.1f mA\"%(I/1e-03);\n",
"\n",
"# Part (b)\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability for free space\n",
"# Since B = mew_o * mew_r * H, solving for mew_r\n",
"mew_r = B/(mew_o*H); #Relative permeability of toroid\n",
"print \"The relative permeability of toroid = %4d\"%mew_r;\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Coil current = 55.3 mA\n",
"The relative permeability of toroid = 5109\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.11, Page 125"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability for free space\n",
"l = 0.15; # Mean length, m\n",
"N = 2500; # Number of turns\n",
"I = 0.3; # Electric current, A\n",
"\n",
"#Calculations\n",
"# Since magnetic field strength is defined as the mmf per metre length of the magnetic circuit, therefore, we have\n",
"H = (N*I)/l; # Magnetic field strength, At/m\n",
"B = 0.75; # Flux density( value taken from graph ), T\n",
"# Since B = ( mew_r * mew_o * H ), solving for mew_r\n",
"mew_r = B/(mew_o * H); # Relative permeability\n",
"\n",
"#Results\n",
"print \"The flux density of given toroid = %3.2f T \"%B\n",
"print \"The relative permeability of given toroid = %5.1f\"%mew_r\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The flux density of given toroid = 0.75 T \n",
"The relative permeability of given toroid = 119.4\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.12, Page 126"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability for free space\n",
"l = 0.1875; # Mean length, m\n",
"A = 8e-05; # Cross- sectional area of of coil, metre-square\n",
"N = 750; # Number of turns\n",
"phi = 112e-06; # Flux, Wb\n",
"l_gap = 0.5e-03; # Average length of the magnetic circuit,m\n",
"B = phi/A; # Flux density, Wb\n",
"H = 2000; # Magnetic field strength( value taken from graph ), At/m\n",
"\n",
"#Calculations\n",
"F_Fe = H*l; # The m.m.f in the iron part of the circuit, At\n",
"# Since F = I*N, solving for I\n",
"I = F_Fe/N; # Coil current under normal conditions, A\n",
"# Since B = mew_o * H_gap, solving for H_gap\n",
"H_gap = B/mew_o; # Magnetic field strength, At/m\n",
"# Since H_gap = F_gap/l_gap, solving for F_gap\n",
"F_gap = H_gap * l_gap; # The mmf in the air part of the circuit, At\n",
"F = F_Fe + F_gap; # Total circuit mmf, At\n",
"I_new = F/N; # Current required to maintain the flux at its original value, A\n",
"\n",
"#Results\n",
"print \"The coil current required to produce a flux of %3d micro-weber in the toroid = %3.1f A \"%(phi/1e-06, I);\n",
"print \"Current required to maintain the flux at its original value = %5.3f A\"%(I_new);\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The coil current required to produce a flux of 112 micro-weber in the toroid = 0.5 A \n",
"Current required to maintain the flux at its original value = 1.243 A\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.13, Page 127"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"l_A = 0.25; # Mean length of circuit A, m\n",
"l_B = 0.15; # Mean length of circuit A, m\n",
"A_A = 11.5e-04; # Cross-sectional area of circuit A, metre-square\n",
"A_B = 12e-04; # Cross-sectional area of circuit B, metre-square\n",
"phi = 1.5e-03; # Flux, Wb\n",
"N = 1000; # Number of turns\n",
"\n",
"#Calculations\n",
"B_A = phi/A_A; # Flux density linked with circuit A, T\n",
"B_B = phi/A_B; # Flux density linked with circuit B, T\n",
"H_A = 1470; # Magnetic field strength of circuit A( value taken from graph ), At/m\n",
"H_B = 845; # Magnetic field strength of circuit B( value taken from graph ), At/m\n",
"# Since H = F/l, solving for F \n",
"F_A = H_A * l_A; # Magnetic field strength of circuit A, At/m\n",
"F_B = H_B * l_B; # Magnetic field strength of circuit B, At/m\n",
"F = F_A + F_B; # Total circuit m.m.f, At/m\n",
"I = F/N; # Coil current, A\n",
"\n",
"#Result\n",
"print \"Coil current in the magnetic circuit = %5.3f A\"%I\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Coil current in the magnetic circuit = 0.494 A\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.14, Page 130"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"A = 8e-04; # Cross-sectional area, metre-square\n",
"d = 24e-02; # Mean diameter of iron ring, m \n",
"phi = 1.2e-03; # Flux, Wb\n",
"mew_r = 1200; # Relative permeability\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability for free space\n",
"mew_air = 1; # Permeability for air\n",
"l_gap = 3e-03; # Mean length, m\n",
"\n",
"#Calculations\n",
"l_Fe = (math.pi) * d; # Mean length of iron circuit, m\n",
"S_Fe = l_Fe/(mew_r * mew_o *A); # Reluctance of iron circuit, At/Wb\n",
"S_gap = l_gap/(mew_air * mew_o *A); # Reluctance of gap, At/Wb\n",
"S = S_Fe + S_gap; # Total circuit reluctance, At/Wb\n",
"# Since phi = F/S, solving for F\n",
"F = phi*S; # Magnetomotive force, At\n",
"\n",
"#Result\n",
"print \"The required mmf = %5.1f At\"%F\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required mmf = 4331.0 At\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.15, Page 130"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"N = 500; # Number of turns on first section's coil\n",
"phi = 2e-03; # Flux produced by first section, Wb\n",
"l_1 = 85e-02; # Length of first section, m\n",
"l_2 = 65e-02; # Length of second section, m\n",
"l_3 = 0.1e-02; # Length of third section, m\n",
"A_1 = 10e-04; # Csa of first section, m^2\n",
"A_2 = 15e-04; # Csa of second section, m^2\n",
"A_3 = 12.5e-04; # Csa of second section, m^2\n",
"mew_o = 4*(math.pi)*1e-07; # Permeability for free space\n",
"mew_r1 = 600; # Relative permeability of first section\n",
"mew_r2 = 950; # Relative permeability of second section\n",
"mew_r3 = 1; # Relative permeability of third section\n",
"\n",
"#Calculations&Results\n",
"# Part (a)\n",
"S_1 = l_1/(mew_r1 * mew_o * A_1); # Reluctance of first section, At/Wb\n",
"S_2 = l_2/(mew_r2 * mew_o * A_2); # Reluctance of first section, At/Wb\n",
"S_3 = l_3/(mew_r3 * mew_o * A_3); # Reluctance of first section, At/Wb\n",
"S = S_1 + S_2 + S_3; # Total reluctance of the circuit, At/Wb\n",
"print \"Total reluctance of the circuit = %4.2fe+06 At/Wb\"%(S*1e-06);\n",
"\n",
"# Part (b)\n",
"# Since phi = F/S, solving for F\n",
"F = phi*S; # Magnetomotive force, At\n",
"# Since F = N*I, solving for I\n",
"I = F/N; # Electric current in first section, A\n",
"print \"Electric current in first section = %4.2f A\"%I\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total reluctance of the circuit = 2.13e+06 At/Wb\n",
"Electric current in first section = 8.51 A\n"
]
}
],
"prompt_number": 16
}
],
"metadata": {}
}
]
}