{
"metadata": {
"name": "",
"signature": "sha256:9ccabd1c0a5d5861a1e63defe760a8b9caed49864d9aebb3ab3b0741ed755b61"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7: Dielectric Properties"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1, Page number 7.23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"C = 2*10**-6 #Capacitance(F)\n",
"V = 1000 #voltage(V)\n",
"Er = 100 #permittivity\n",
"\n",
"#Calculations\n",
"W = (C*V**2)/2\n",
"\n",
"Co = C/Er\n",
"Wo = (Co*V**2)/2\n",
"Wf = W-Wo\n",
"\n",
"#Result\n",
"print \"Energy stored in condenser =\",W,\"J\"\n",
"print \"Energy stored in polarizing the dilectric =\",Wf,\"J\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Energy stored in condenser = 1.0 J\n",
"Energy stored in polarizing the dilectric = 0.99 J\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2, Page number 7.24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaraion\n",
"Er = 4.94 #permittivity\n",
"n2 = 2.69 #index of refraction\n",
"\n",
"#Calculations\n",
"'''\n",
"Er - 1 N(ae+ai)\n",
"------ = ---------\n",
"Er + 2 3*Eo \n",
"Sunbstituting the values for Er, we get,\n",
"N(ae+ai) \n",
"-------- = 0.5677 ------------(1)\n",
" 3*ao\n",
"'''\n",
"x = 0.5677\n",
"\n",
"'''\n",
"Also, Er = n**2\n",
"Therefore, n**2-1 N*ae\n",
" ------- = -----\n",
" n**2+2 3*Eo\n",
"Substituting the values for n^2, we get,\n",
"N*ae\n",
"---- = 0.36034 ---------------(2)\n",
"3*Eo\n",
"'''\n",
"y = 0.36034\n",
"#Let z = ai/ae\n",
"#Dividing equation (1) by (2), we get,\n",
"\n",
"z = (x/y)-1\n",
"\n",
"#Result\n",
"print \"Ratio between electronic and ionic probabbility is\",round(z,3) ,\"or\",round((1/z),3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio between electronic and ionic probabbility is 0.575 or 1.738\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3, Page number 7.25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"Er = 2.56 #permittivity\n",
"f = 1*10**6 #frequency(Hz)\n",
"A = 8*10**-4 #area(m^2)\n",
"d= 0.08*10**-3 #distance of seperation(m)\n",
"Eo = 8.85*10**-12\n",
"\n",
"#Calculations\n",
"Er_dash = Er*0.7*10**-4\n",
"w = 2*math.pi*f\n",
"Rp = d/(w*Eo*Er_dash*A)\n",
"\n",
"Cp = (A*Eo*Er)/d\n",
"\n",
"#Results\n",
"print \"Parallel loss resistance =\",round((Rp/1E+6),2),\"MOhms\"\n",
"print \"Capacitance =\",Cp,\"F(Calculation mistake in textbook)\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Parallel loss resistance = 10.04 MOhms\n",
"Capacitance = 2.2656e-10 F(Calculation mistake in textbook)\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5, Page number 7.26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Varaible declaration\n",
"N = 3.*10**28 #density(atoms/m^3)\n",
"ae = 10.**-40 #electronic polarizability(F m^2)\n",
"Eo = 8.854*10**-12 #permittivity of free space(F/m)\n",
"\n",
"#Calculaion\n",
"Er = 1+((N*ae)/Eo)\n",
"\n",
"#Result\n",
"print \"dielectric constant =\",round(Er,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"dielectric constant = 1.339\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5, Page number 7.26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"Er = 1.0000684 #permittivity of dilectric\n",
"Eo = 8.854*10**-12 #permittivity of free space(F/m)\n",
"N = 2.7*10**25 #density(atoms/m^3)\n",
"\n",
"#Calculation\n",
"ae = (Eo*(Er-1))/N\n",
"\n",
"#Result\n",
"print \"Electronic polarizability =\",round((ae/1E-41),3),\"*10^-41 Fm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Electronic polarizability = 2.243 *10^-41 Fm^2\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6, Page number 7.27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"A = 100*10**-4 #area of parallel capacitor(m^2)\n",
"d = 1*10**-2 #separation between plates(m)\n",
"Eo = 8.854*10**-12 #permittivity of free space(F/m)\n",
"V = 100 #voltage(V)\n",
"\n",
"#Calculation\n",
"C = (Eo*A)/d\n",
"Q = C*V\n",
"\n",
"#Result\n",
"print \"Capacitance =\",round((C/1E-12),2),\"pF\"\n",
"print \"Charge =\",Q,\"C\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Capacitance = 8.85 pF\n",
"Charge = 8.854e-10 C\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7, Page number 7.28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"N = 6.02*10**26 #Avogadro's number\n",
"den = 2050 #density(kg/m^3)\n",
"Ma = 32 #atomic weight\n",
"Eo = 8.55*10**-12 #permittivity of free space(F/m)\n",
"v = 1/3 #internal field constant\n",
"Er = 3.75 #dielectric constant of sulphur\n",
"\n",
"#Calculations\n",
"n = (N*den)/Ma #no. of atoms per m^3\n",
"ae = ((Er-1)/(Er+2))*((3*Eo)/n)\n",
"\n",
"#Result\n",
"print \"Electronic polarizability =\",round((ae/1E-40),3),\"*10^-41 Fm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Electronic polarizability = 3.181 *10^-41 Fm^2\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}