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{
"metadata": {
"name": "",
"signature": "sha256:2693d83b10c8e62fc8d3ef78c9959c4d8327c36ed1f7884372585d33796bcbc3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"2: Electromagnetic Theory"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 2.1, Page number 46"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#importing modules\n",
"from __future__ import division\n",
"from sympy import *\n",
"import math\n",
"\n",
"#Variable declaration\n",
"C = 10; #Capacitance of the capacitor(pF)\n",
"#given V=0.2*sin(120*math.pi*t) in volts\n",
"\n",
"#Calculation\n",
"C=C*10**-12; #Capacitance of the capacitor(F)\n",
"x, y, z, t = symbols('x y z t')\n",
"k, m, n = symbols('k m n', integer=True)\n",
"f, g, h = symbols('f g h', cls=Function)\n",
"#I = C*dV/dt\n",
"#let dV/dt be a\n",
"a=diff(0.2*sin(120*math.pi*t),t) #dV/dt\n",
"#value of dV/dt is 75.398223686155*cos(376.991118430775*t)\n",
"#for cosine function peak value occurs when 120*math.pi*t = 0\n",
"#therefore value of dV/dt becomes d = 75.398223686155\n",
"d = 75.398223686155; #value of dV/dt \n",
"I=C*d; #displacement current(A)\n",
"\n",
"#Result\n",
"print \"value of dV/dt is\",a\n",
"print \"displacement current is\",I, \"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"value of dV/dt is 75.398223686155*cos(376.991118430775*t)\n",
"displacement current is 7.53982236862e-10 A\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 2.2, Page number 46"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#importing modules\n",
"from __future__ import division\n",
"from sympy import *\n",
"import math\n",
"\n",
"#Variable declaration\n",
"epsilon_r = 1; #Relative electrical permittivity of free space\n",
"epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n",
"#given E=sin(120*math.pi*t) in volts\n",
"\n",
"#Calculation\n",
"x, y, z, t = symbols('x y z t')\n",
"k, m, n = symbols('k m n', integer=True)\n",
"f, g, h = symbols('f g h', cls=Function)\n",
"#J2 = epsilon*dE/dt\n",
"epsilon=epsilon_0*epsilon_r;\n",
"#let dE/dt be a\n",
"a=diff(sin(120*math.pi*t),t) #dE/dt\n",
"#value of dE/dt is 376.991118430775*cos(376.991118430775*t)\n",
"#for cosine function peak value occurs when 120*math.pi*t = 0\n",
"#therefore value of dE/dt becomes d = 376.991118430775\n",
"d = 376.991118430775; #value of dE/dt\n",
"J2=epsilon*d; #displacement current density(A/m**2)\n",
"\n",
"#Result\n",
"print \"value of dE/dt is\",a\n",
"print \"The peak value of displacement current density is\",J2, \"A/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"value of dE/dt is 376.991118430775*cos(376.991118430775*t)\n",
"The peak value of displacement current density is 3.33787936259e-09 A/m**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 2.3, Page number 47 (Theoritical proof)"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 2.4, Page number 47"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"p = 60; #Power rating of bulb(W)\n",
"d = 0.5; #Distance from the bulb(m)\n",
"\n",
"#Calculation\n",
"A=4*math.pi*d**2; #area(m**2)\n",
"P = p/A; #Value of Poynting vector(W/m**2)\n",
"P = math.ceil(P*100)/100; #rounding off value of P to 1 decimal\n",
"\n",
"#Result\n",
"print \"The value of Poynting vector is\",P, \"W/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of Poynting vector is 19.1 W/m**2\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 2.5, Page number 47"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"E_peak = 6; #Peak value of electric field intensity(V/m)\n",
"c = 3*10**8; #Speed of electromagnetic wave in free space(m/s)\n",
"mew_0 = 4*math.pi*10**-7; #Absolute permeability of free space(Tm/A)\n",
"epsilon_0 = 8.854*10**-12; #Absolute permittivity of free space(F/m)\n",
"mew_r = 1; #Relative permeability of medium\n",
"epsilon_r = 3; #Relative permittivity of the medium\n",
"\n",
"#Calculation\n",
"v = c/math.sqrt(mew_r*epsilon_r); #Wave velocity(m/s)\n",
"v = v/10**8;\n",
"v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n",
"eta = math.sqrt((mew_0/epsilon_0)*(mew_r/epsilon_r)); #Intrinsic impedance of the medium(ohm)\n",
"eta = math.ceil(eta*10)/10; #rounding off the value of v to 1 decimal\n",
"H_P = E_peak/eta; #Peak value of the magnetic intensity(A/m)\n",
"H_P = H_P*10**2;\n",
"H_P = math.ceil(H_P*10**2)/10**2; #rounding off the value of v to 2 decimals\n",
"\n",
"#Result\n",
"print \"The wave velocity is\",v,\"*10**8 m/s\"\n",
"print \"The intrinsic impedance of the medium is\",eta, \"ohm\"\n",
"print \"The peak value of the magnetic intensity is\",H_P,\"*10**-2 A/m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wave velocity is 1.7321 *10**8 m/s\n",
"The intrinsic impedance of the medium is 217.6 ohm\n",
"The peak value of the magnetic intensity is 2.76 *10**-2 A/m\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
