{
"metadata": {
"name": "",
"signature": "sha256:ca10cc57956bed4f1b4d18744134bc27c9e2980c82af910dabf566547448b24f"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter3:DIELECTRIC PROPERTIES OF MATERIALS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg1:pg-119"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Eg=6.0 #dielectric constant of glass plate\n",
"dg=0.25 #thickness of glass plate in mm\n",
"Ep=3.0 #dielectric constant of plastic film\n",
"dp=0.1 #thickness of plastic film in mm\n",
"Eo=8.85e-12 #permittivity of free space in F/m \n",
"A=1 #let surface area be 1\n",
"Cg=Eg*Eo*A/dg\n",
"Cp=Ep*Eo*A/dp\n",
"ratio=Cg/Cp\n",
"print\"Cg = \",ratio,\"Cp\"\n",
"print\"Since Cp>Cg,the plastic film filled capacitor holds more charge than the glass plate filled capacitor\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cg = 0.8 Cp\n",
"Since Cp>Cg,the plastic film filled capacitor holds more charge than the glass plate filled capacitor\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg2:pg-120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Er=2.8 #dielectric constant of a dielectric material\n",
"D=3e-8 #magnitude of electric displacement vector in C/m**2\n",
"p=(Er-1)*D/Er\n",
"print\"Polarization is \",round(p,10),\"C/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Polarization is 1.93e-08 C/m**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg3:pg-120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"E=1000 #electric field in V/m\n",
"p=4.3e-8 #polarization in C/m**2\n",
"Eo=8.85e-12#permittivity of free space in F/m \n",
"Er=1+(p/(Eo*E))\n",
"print\"Relative permittivity of NaCl is \",round(Er,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Relative permittivity of NaCl is 5.86\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg4:pg-120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Er=1.000074 #dielectric constant of helium \n",
"Eo=8.85e-12 #permittivity of free space in F/m (in book F/m2 is printed which is wrong)\n",
"E=100 #electric field in V/m\n",
"Na=6e23 #Avogadro number\n",
"V=22.4 #volume occupied by 1gm atom of gas at NTP in litres\n",
"N=Na/(V*1e-3)\n",
"p=Eo*(Er-1)*E\n",
"P=p/N\n",
"print\"Induced dipole moment is \",round(P,42),\"Cm\"#answer in book is in different form as 24.42e-40 Cm"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Induced dipole moment is 2.445e-39 Cm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg5:pg-121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Epsilon=1.46e-10 #permittivity of diamond in C**2/Nm**2\n",
"Eo=8.86e-12 #permittivity of free space in C**2/Nm**2\n",
"Er=Epsilon/Eo \n",
"X=Eo*(Er-1)\n",
"print\"Dielectric constant is \",round(Er,2)\n",
"print\"Electrical susceptibility is \",round(X,12),\"C**2/Nm**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dielectric constant is 16.48\n",
"Electrical susceptibility is 1.37e-10 C**2/Nm**2\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6:pg-121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Xe=35.4e-12 #electrical susceptibility in C**2/Nm**2\n",
"Eo=8.85e-12 #permittivity of free space in C**2/Nm**2 \n",
"K=1+(Xe/Eo)\n",
"Epsilon=Eo*K\n",
"print\"Dielectric constant is \",int(K)\n",
"print\"Permittivity of the material is \",Epsilon,\"C**2/Nm**2\"\n",
"#answer in book is in different form as 44.25e-12 C**2/Nm**2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dielectric constant is 5\n",
"Permittivity of the material is 4.425e-11 C**2/Nm**2\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg7:pg-121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Vo=60 #applied potential difference in volt\n",
"V=30 #reduced potential difference in volt\n",
"K=Vo/V\n",
"print\"Dielectric constant of the liquid is \",K"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dielectric constant of the liquid is 2\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg8:pg-121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Vo=100 #potential difference in volts\n",
"t=0.3 #thickness of insulator in cm\n",
"A=100 #area in cm**2\n",
"d=1 #separation between plates in cm\n",
"K=7 #dielectric constant \n",
"Eo=8.9e-12 #permittivity of free space in C**2/Nm**2\n",
"E_o=Vo/(d*1e-2)\n",
"E=E_o/K\n",
"D=K*Eo*E\n",
"p=(K-1)*Eo*E\n",
"print\"E = \",\"{:.2e}\".format(E),\"Volt/m\"\n",
"print\"D = \",D,\"C/m**2\"\n",
"print\"p = \",round(p,9),\"C/m**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"E = 1.43e+03 Volt/m\n",
"D = 8.9e-08 C/m**2\n",
"p = 7.6e-08 C/m**2\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg9:pg-122"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"E=6e4 #electric field in V/m\n",
"K=1.000134 #dielectric constant of neon\n",
"Eo=8.9e-12 #permittivity of free space in F/m\n",
"Na=6e23 #Avogadro number\n",
"V=22.4 #volume occupied by 1gm atom of gas at NTP in litres\n",
"p=Eo*(K-1)*E\n",
"N=Na/(V*1e-3)\n",
"P=p/N\n",
"alpha=P/(Eo*E)\n",
"print\"Induced dipole moment is\",round(P,38),\"Cm\"\n",
"print\"Atomic polarizability of neon is \",round(alpha,32),\"m**3\"\n",
"#answer in book is wrong"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Induced dipole moment is 2.67e-36 Cm\n",
"Atomic polarizability of neon is 5e-30 m**3\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg11:pg-123"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Er=1.0024 #dielectric constant of argon atom\n",
"N=2.7e25 #number of atoms per cubic meter\n",
"Eo=8.85e-12 #permittivity of free space in F/m\n",
"alpha_e=Eo*(Er-1)/N\n",
"print\"Electronic polarizability is \",round(alpha_e,41),\"Fm**2\"\n",
"#answer is wrong in book"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Electronic polarizability is 7.9e-40 Fm**2\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg12:pg-123"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"N=9.8e26 #number of atoms in volume of one cubic meter of hydrogen gas\n",
"Eo=8.85e-12 #permittivity of free space in F/m\n",
"ao=0.53e-10 #radius of hydrogen atom in meter\n",
"alpha=4*math.pi*Eo*ao**3\n",
"Er=1+(4*math.pi*N*ao**3)\n",
"print\"Polarizability is \",round(alpha,43),\"Fm**2\"\n",
"print\"Relative permittivity is \",round(Er,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Polarizability is 1.66e-41 Fm**2\n",
"Relative permittivity is 1.0018\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg13:pg-124"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"alpha_300=2.5e-39 # total polarizability in C**2m/N at 300 K\n",
"alpha_400=2.0e-39 # total polarizability in C**2m/N at 400 K\n",
"T1 =300 # temperature in Kelvin\n",
"T2 =400 # temperature in Kelvin\n",
"beta=(alpha_300-alpha_400)*(T1*T2/(T2-T1))\n",
"alpha_def_300=alpha_300 - beta/300\n",
"alpha_oriant_300=beta/300\n",
"alpha_oriant_400=beta/400\n",
"print\"Deformational Polarizability is \",alpha_def_300,\"C**2mN**-1\"\n",
"print\"Orientational Polarizability at %d K is \"%T1,alpha_oriant_300,\"C**2mN**-1\"\n",
"print\"Orientational Polarizability at %d K is \"%T2,alpha_oriant_400,\"C**2mN**-1\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Deformational Polarizability is 5e-40 C**2mN**-1\n",
"Orientational Polarizability at 300 K is 2e-39 C**2mN**-1\n",
"Orientational Polarizability at 400 K is 1.5e-39 C**2mN**-1\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg14:pg-132"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m=32 # Atomic weight of sulphur\n",
"d=2.08 # Density in g/cm**3\n",
"alpha_e=3.28e-40 # Electronic polarizability in Fm**2\n",
"Na=6.023e23 # Avogadro Number\n",
"Eo=8.85e-12 # Permittivity of free space in F/m\n",
"N=Na*d*1e6/m \n",
"k=N*alpha_e/(3*Eo)\n",
"epsilon_r = (1+ k*2)/(1-k)# Calculation of relative permittivity\n",
"print\"Relative dielectric constant is \",round(epsilon_r,1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Relative dielectric constant is 3.8\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg15:pg-132"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n=1.5 # Refractive index\n",
"Er=5.6 # Static dielectric constant\n",
"per=(1-((n**2-1)/(n**2+2))*(Er+2)/(Er-1))*100 # Pecentage of ionic polarizability\n",
"print\"Percentage of ionic polarizability is \",round(per,1),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Percentage of ionic polarizability is 51.4 %\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg16:pg-133"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n=sqrt(2.69) # Refractive index\n",
"Er=4.94 # Static dielectric constant\n",
"k1=(Er-1)/(Er+2)\n",
"k2=(n**2-1)/(n**2+2)\n",
"ratio=1/round(((k1/k2)-1),3) \n",
"print\"Ratio of electronic to ionic polarizability is \",round(ratio,3)\n",
"#in book ai/ae is mentioned instead of ae/ai in final answer which is wrong"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of electronic to ionic polarizability is 1.736\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg17:pg-133"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Er=6.75 #dielectric constant of glass\n",
"n=1.5 #refractive index of glass\n",
"f=1e9 #frequency in Hz\n",
"per=(Er-n**2)*100/(Er-1)\n",
"print\"Percentage attributed to ionic polarizability is \",round(per,1),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Percentage attributed to ionic polarizability is 78.3 %\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg18:pg-142"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"t=5.5e-3 #thickness of quartz crystal plate in meter\n",
"p=2.65e3 #density of quartz crystal in Kg/m**3\n",
"Y=8e10 #Young's modulus of quartz in N/m**2 (value is wrong in question in book)\n",
"m=1 \n",
"f=m*sqrt(Y/p)/(2*t)\n",
"print\"Frequency is \",int(f*1e-3),\"KHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frequency is 499 KHz\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg19:pg-148"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import cmath\n",
"Er=4.36 #real part of dielectric constant of bakelite\n",
"N=4e28 #number of atoms per cubic meter\n",
"tan_d=2.8e-2#loss tangent at 1 MHz freuqency\n",
"Eo=8.853e-12#permittivity of free space in F/m\n",
"alpha=(3*Eo/N)*(Er*(1-(1j*tan_d))-1)/(Er*(1-(1j*tan_d))+2)\n",
"x=round(alpha.real*1e40,1)\n",
"y=round(alpha.imag*1e40,2)\n",
"alpha=complex(x,y)\n",
"print\"Complex polarizability is \",alpha*1e-40,\"Fm**2\"\n",
"#in book answer is in different form and as (3.5-0.06i)*10**-40\n",
"#in book unit of answer is not mentioned"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Complex polarizability is (3.5e-40-6e-42j) Fm**2\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg20:pg-149"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"t=18e-6 # Relaxation time in second\n",
"Er_d=1 # let real part of dielectric constant be 1\n",
"Er_dd=1 # let imaginary part of dielectric constant be 1\n",
"f=1/(2*math.pi*t) # Calculation of frequency\n",
"delta=math.atan(Er_dd/Er_d)\n",
"phi=90-(delta*180/math.pi) # Calculation of phase difference\n",
"print\"Frequency is \",round(f/1e3,1),\"KHz\"\n",
"print\"Phase difference between current and voltage is %d degree\"%(phi)\n",
"print\"Current leads the voltage \"#this part is not mentioned in answer in book"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frequency is 8.8 KHz\n",
"Phase difference between current and voltage is 45 degree\n",
"Current leads the voltage \n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}