{
"metadata": {
"name": "",
"signature": "sha256:df8ccdc39cf4228aa502def88be8b0eaa1a1170d675814e78e23ede418957e6f"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"7: Electromagnetic Induction"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.1, Page number 204"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"R=125; #resistance(ohm)\n",
"V=3*10**-4; #potential difference(V)\n",
"T=10; #time period(sec)\n",
"theta1=16*10**-2; #deflection(m)\n",
"theta=5*10**-2; #deflection(m)\n",
"\n",
"#Calculation\n",
"i=V/R; #current(A)\n",
"q=T*i*theta/(2*math.pi*theta1); #charge(C)\n",
"\n",
"#Result\n",
"print \"charge is\",round(q*10**6,3),\"*10**-6 C\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"charge is 1.194 *10**-6 C\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.2, Page number 205"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"T=8; #time period(s)\n",
"i=2*10**-6; #current(A)\n",
"theta1=1;\n",
"theta=1;\n",
"\n",
"#Calculation\n",
"q=T*i*theta/(2*math.pi*theta1); #charge(C)\n",
"\n",
"#Result\n",
"print \"charge is\",round(q*10**6,3),\"*10**-6 C\"\n",
"print \"answer varies due to rounding off errors\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"charge is 2.546 *10**-6 C\n",
"answer varies due to rounding off errors\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.3, Page number 205"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"l=1.8*10**-2; #length(m)\n",
"B=0.5; #magnitude of field(Wb/m**2)\n",
"N=200; #number of turns\n",
"t=0.8; #time period(sec)\n",
"R=12; #resistance(ohm)\n",
"\n",
"#Calculation\n",
"A=l**2; #area of coil(m**2)\n",
"phiB=B*A; #magnetic flux in coil(Wb)\n",
"e=N*(phiB-0)/t; #induced emf(V)\n",
"i=e/R; #current(A)\n",
"\n",
"#Result\n",
"print \"induced emf is\",e,\"V\"\n",
"print \"current is\",i*10**4,\"*10**-4 A\"\n",
"print \"answers given in the book are wrong\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"induced emf is 0.0405 V\n",
"current is 33.75 *10**-4 A\n",
"answers given in the book are wrong\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.6, Page number 207"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"B=100*10**-4; #magnetic field(Wb/m**2)\n",
"d=20*10**-2; #diameter(m)\n",
"n=10; #number of rotations\n",
"\n",
"#Calculation\n",
"r=d/2; #radius(m)\n",
"dAbydt=math.pi*n*(r**2); #area(turns m**2/s)\n",
"e=B*dAbydt; #potential difference(V)\n",
"\n",
"#Result\n",
"print \"potential difference is\",round(e*10**3,3),\"mV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"potential difference is 3.142 mV\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.7, Page number 207"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"l=1; #length(m)\n",
"B=0.2; #magnetic field(Wb/m**2)\n",
"v=0.8; #velocity(m/s)\n",
"theta1=60*math.pi/180; #angle(radian)\n",
"theta2=45*math.pi/180; #angle(radian)\n",
"theta3=30*math.pi/180; #angle(radian)\n",
"\n",
"#Calculation\n",
"e1=B*l*v*math.sin(theta1); #induced emf when B and v are perpendicular(V)\n",
"e2=B*l*v*math.sin(theta1)*math.sin(theta2); #induced emf with angle 45 degrees(V)\n",
"e3=B*l*v*math.sin(theta1)*math.sin(theta2)*math.sin(theta3); #induced emf with angle 30 degrees(V)\n",
"\n",
"#Result\n",
"print \"induced emf when B and v are perpendicular is\",round(e1,4),\"V\"\n",
"print \"induced emf with angle 45 degrees is\",round(e2,3),\"V\"\n",
"print \"induced emf with angle 30 degrees is\",round(e3,3),\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"induced emf when B and v are perpendicular is 0.1386 V\n",
"induced emf with angle 45 degrees is 0.098 V\n",
"induced emf with angle 30 degrees is 0.049 V\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.8, Page number 208"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"L=20; #inductance(H)\n",
"i=0.1; #current(A)\n",
"\n",
"#Calculation\n",
"Ub=(1/2)*L*(i**2); #energy stored in inductor(J)\n",
"\n",
"#Result\n",
"print \"energy stored in inductor is\",Ub,\"J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy stored in inductor is 0.1 J\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.9, Page number 209"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e=12; #induced emf(V)\n",
"L=53*10**-3; #inductance(H)\n",
"R=0.35; #resistance(ohm)\n",
"\n",
"#Calculation\n",
"i=e/R; #current(A)\n",
"Ub=(1/2)*L*(i**2); #energy stored in inductor(J)\n",
"\n",
"#Result\n",
"print \"energy stored in inductor is\",round(Ub,1),\"J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy stored in inductor is 31.2 J\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.10, Page number 209"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N=1250; #number of turns\n",
"a=5.2*10**-2; #length(m)\n",
"b=9.5*10**-2; #breadth(m)\n",
"h=1.3*10**-2; #height(m)\n",
"mew0=4*math.pi*10**-7; \n",
"\n",
"#Calculation\n",
"L=(mew0*(N**2)*h*math.log(b/a))/(2*math.pi); #inductance(H)\n",
"\n",
"#Result\n",
"print \"inductance is\",round(L*10**3,1),\"mH\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"inductance is 2.4 mH\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.11, Page number 209"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N1=500; #number of turns\n",
"A=3*10**-3; #area(m**2)\n",
"l=0.5; #length(m)\n",
"mew0=4*math.pi*10**-7; \n",
"N2=8; #number of turns\n",
"\n",
"#Calculation\n",
"M=mew0*N1*N2*A/l; #coefficient of mutual induction(H)\n",
"\n",
"#Result\n",
"print \"coefficient of mutual induction is\",round(M*10**6),\"micro H\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"coefficient of mutual induction is 30.0 micro H\n"
]
}
],
"prompt_number": 29
}
],
"metadata": {}
}
]
}