10: Dielectric Properties

Example number 10.1, Page number 276

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration    
P=4.3*10**-8;     #polarisation(per cm**2)
epsilon0=8.85*10**-12;        #relative permeability(F/m)
E=1000;         #electric field(V/m)

#Calculations
epsilonr=1+(P/(epsilon0*E));        #relative permittivity

#Result
print "relative permittivity is",round(epsilonr,2)

relative permittivity is 5.86

Example number 10.2, Page number 276

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration    
k=4;
epsilon0=9*10**-12;        #relative permeability(F/m)
E=10**6;         #electric field(V/m)

#Calculations
D=k*epsilon0*E;     #electric displacement(C/m**2)
P=epsilon0*E*(k-1);      #polarisation(C/m**2)

#Result
print "electric displacement is",int(D*10**6),"*10**-6 C/m**2"
print "polarisation is",int(P*10**6),"*10**-6 C/m**2"

electric displacement is 36 *10**-6 C/m**2
polarisation is 27 *10**-6 C/m**2

Example number 10.3, Page number 277

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration    
k=5;
epsilon0=8.86*10**-12;        #relative permeability(F/m)
D=5*10**-12;        #electric displacement(C/m**2)
V=0.5*10**-6;

#Calculations
E=D/(k*epsilon0);     #electric field(N/C)
P=D*(1-(1/k));      #polarisation(C/m**2)
dm=P*V;        #induced dipole moment(cm)

#Result
print "electric field is",round(E,3),"N/C"
print "polarisation is",P,"C/m**2"
print "induced dipole moment is",dm,"cm"

electric field is 0.113 N/C
polarisation is 4e-12 C/m**2
induced dipole moment is 2e-18 cm

Example number 10.4, Page number 277

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration    
k=1.000074;
epsilon0=8.85*10**-12;        #relative permeability(F/m)
E=1;               #electric field(N/C)
n=2.69*10**25;     #molecular density

#Calculations
p=epsilon0*E*(k-1)/n;    #dipole moment(coulx metre)

#Result
print "dipole moment is",round(p*10**41,2),"*10**-41 coul x metre"

dipole moment is 2.43 *10**-41 coul x metre

Example number 10.5, Page number 278

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration    
k=1.000134;
epsilon0=8.85*10**-12;        #relative permeability(F/m)
E=90000;               #electric field(N/C)
N=6.023*10**26;       #avagadro number

#Calculations
n=N/22.4;
p=epsilon0*E*(k-1)/n;    #dipole moment(coul-metre)
alpha=p/E;    #atomic polarizability(coul-m**2/volt)

#Result
print "dipole moment is",round(p*10**36,2),"*10**-36 coul-metre"
print "atomic polarizability is",round(alpha*10**41,1),"*10**-41 coul-m**2/volt"

dipole moment is 3.97 *10**-36 coul-metre
atomic polarizability is 4.4 *10**-41 coul-m**2/volt

Example number 10.6, Page number 278

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration    
k=7;
epsilon0=8.9*10**-12;        #relative permeability(F/m)
V0=100;        #potential difference(V)
d=10**-2;      #displacement(m)

#Calculations
E0=V0/d;       #electric field intensity(volt/m)
E=E0/k;     #electric field(N/C)
D=k*E*epsilon0;       #electric displacement(C/m**2)
p=epsilon0*E*(k-1);    #dipole moment(coul-metre)

#Result
print "electric field is",round(E/10**3,2),"*10**3 volt/m"
print "electric displacement is",D,"C/m**2"
print "dipole moment is",round(p*10**8,1),"*10**-8 C/m**2"

electric field is 1.43 *10**3 volt/m
electric displacement is 8.9e-08 C/m**2
dipole moment is 7.6 *10**-8 C/m**2

Example number 10.7, Page number 279

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;        #relative permeability(F/m)
chi=35.4*10**-12;     #electric susceptibility(coul**2/nt-m**2)

#Calculations
k=1+(chi/epsilon0);      #dielectric constant
epsilon=epsilon0*k;      #permittivity(coul**2/nt-m**2) 

#Result
print "dielectric constant is",k
print "permittivity is",round(epsilon*10**12,2),"*10**-12 coul**2/nt-m**2"

dielectric constant is 5.0
permittivity is 44.25 *10**-12 coul**2/nt-m**2

Example number 10.8, Page number 279

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;        #relative permeability(F/m)
E=100;               #electric field(N/C)
epsilonr=1.000074;   #dielectric constant
n=2.68*10**27;      #density

#Calculations
p=epsilon0*E*(epsilonr-1)/n;    #dipole moment(coul-metre)

#Result
print "dipole moment is",round(p*10**41,4),"*10**-41 C/m**2"
print "answer in the book is wrong"

dipole moment is 2.4437 *10**-41 C/m**2
answer in the book is wrong

Example number 10.9, Page number 287

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;        #relative permeability(F/m)
R=0.053*10**-9;      #radius(nm)
N=9.8*10**26;     #number of atoms

#Calculations
alphae=4*math.pi*epsilon0*R**3;    #electronic polarizability(Fm**2)
epsilonr=1+(4*math.pi*N*R**3);     #relative permittivity

#Result
print "electronic polarizability is",round(alphae*10**41,4),"*10**-41 Fm**2"
print "relative permittivity is",round(epsilonr,4)

electronic polarizability is 1.6557 *10**-41 Fm**2
relative permittivity is 1.0018

Example number 10.10, Page number 288

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;        #relative permeability(F/m)
epsilonr=1.0000684;       #dielectric constant
N=2.7*10**25;     #number of atoms

#Calculations
alphae=epsilon0*(epsilonr-1)/N;    #electronic polarizability(Fm**2)

#Result
print "electronic polarizability is",alphae,"Fm**2"
print "answer varies due to rounding off errors"

electronic polarizability is 2.242e-41 Fm**2
answer varies due to rounding off errors

Example number 10.11, Page number 288

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.854*10**-12;        #relative permeability(F/m)
alphae=10**-40;       #dielectric polarizability(Fm**2)
N=3*10**28;     #number of atoms

#Calculations
epsilonr=1+(N*alphae/epsilon0);    #dielectric constant

#Result
print "dielectric constant is",round(epsilonr,3)

dielectric constant is 1.339

Example number 10.12, Page number 288

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;        #relative permeability(F/m)
epsilonr=1.0024;       #dielectric constant
N=2.7*10**25;     #number of atoms

#Calculations
alphae=epsilon0*(epsilonr-1)/N;    #electronic polarizability(Fm**2)

#Result
print "electronic polarizability is",round(alphae*10**40,1),"*10**-40 Fm**2"
print "answer in the book is wrong"

electronic polarizability is 7.9 *10**-40 Fm**2
answer in the book is wrong

Example number 10.13, Page number 289

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilonr=1.0000684;       #dielectric constant
N=2.7*10**25;     #number of atoms
X=1/(9*10**9);
E=10**6;        #electric field(V/m)
Z=2;     #atomic number
e=1.6*10**-19;         #electron charge(coulomb)

#Calculations
R=((epsilonr-1)/(4*math.pi*N))**(1/3);     #radius of electron cloud(m)
x=X*E*R**3/(Z*e);         #displacement(m)

#Result
print "radius of electron cloud is",round(R*10**11,2),"*10**-11 m"
print "displacement is",round(x*10**17,5),"*10**-17 m"

radius of electron cloud is 5.86 *10**-11 m
displacement is 6.99987 *10**-17 m

Example number 10.14, Page number 293

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;       #dielectric constant
N=3*10**28;     #number of atoms
alphae=10**-40;       #dielectric polarizability(Fm**2)

#Calculations
x=N*alphae/(3*epsilon0);
epsilonr=(1+(2*x))/(1-x);       #dielectric constant

#Result
print "dielectric constant is",round(epsilonr,2)

dielectric constant is 1.38

Example number 10.15, Page number 294

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;       #dielectric constant
Na=6.023*10**26;     #number of atoms
M=32;       #atomic mass
alphae=3.28*10**-40;       #dielectric polarizability(Fm**2)
rho=2.08*10**3;         #density(kg/m**3)

#Calculations
x=Na*rho*alphae/(M*3*epsilon0);
epsilonr=(1+(2*x))/(1-x);       #dielectric constant

#Result
print "dielectric constant is",round(epsilonr,1)

dielectric constant is 3.8

Example number 10.16, Page number 294

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilon0=8.85*10**-12;       #dielectric constant
Na=6.02*10**26;     #number of atoms
epsilonr=3.75;       #dielectric constant
M=32;       #atomic mass
rho=2050;         #density(kg/m**3)
gama=1/3;       #internal field constant

#Calculations
N=Na*rho/M;     #number of atoms
alphae=((epsilonr-1)/(epsilonr+2))*(3*epsilon0/N);       #electronic polarizability(Fm**2)

#Result
print "electronic polarizability is",round(alphae*10**40,2),"*10**-40 Fm**2"

electronic polarizability is 3.29 *10**-40 Fm**2

Example number 10.17, Page number 295

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilonr=4.94;       #dielectric constant
n2=2.69;

#Calculations
x=(epsilonr-1)/(epsilonr+2);
y=(n2-1)/(n2+2);
alpha=1/((x/y)-1);       #ratio between electronic and ionic polarizability

#Result
print "ratio between electronic and ionic polarizability is",round(alpha,3)

ratio between electronic and ionic polarizability is 1.738

Example number 10.18, Page number 296

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration    
epsilonr=5.6;       #dielectric constant
n=1.5;

#Calculations
x=(epsilonr+2)/(epsilonr-1);
y=(n**2-1)/(n**2+2);
alpha=(1-(x*y))*100;       #percentage of ionic polarizability

#Result
print "percentage of ionic polarizability is",round(alpha,1),"%"

percentage of ionic polarizability is 51.4 %