7: Dielectrics

Example number 7.1, Page number 146

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

#Variable declaration
epsilonr=3.75;       #relative dielectric constant
T=27;    #temperature(C)
gama=1/3;     #internal field constant
rho=2050;     #density(kg/m**3)
Ma=32;        #atomic weight(amu)
Na=6.022*10**23;     #avagadro number
epsilon0=8.85*10**-12;    

#Calculation
x=(epsilonr-1)/(epsilonr+2);
alpha_e=x*Ma*3*epsilon0/(rho*Na);     #electronic polarisability(Fm**2)

#Result
print "electronic polarisability is",round(alpha_e*10**37,3),"*10**-37 Fm**2"
print "answer varies due to rounding off errors"

electronic polarisability is 3.291 *10**-37 Fm**2
answer varies due to rounding off errors

Example number 7.2, Page number 146

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=100*10**-4;      #area(m**2)
epsilon0=8.85*10**-12;    
d=1*10**-2;     #seperation(m)
V=100;     #potential(V)

#Calculation
C=A*epsilon0/d;     #capacitance(PF)
Q=C*V;         #charge on plates(C)

#Result
print "capacitance is",C*10**12,"PF"
print "charge on plates is",Q,"C"

capacitance is 8.85 PF
charge on plates is 8.85e-10 C

Example number 7.3, Page number 147

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

#Variable declaration
epsilonr=1.0000684;     #dielectric constant
N=2.7*10**25;   #number of atoms
epsilon0=8.85*10**-12;    

#Calculation
alpha_e=epsilon0*(epsilonr-1)/N;    #polarisability(Fm**2)

#Result
print "polarisability is",alpha_e,"Fm**2"
print "answer varies due to rounding off errors"

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

Example number 7.4, Page number 147

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
alpha_e=10**-40;      #polarisability(Fm**2)
N=3*10**28;    #density of atoms
epsilon0=8.85*10**-12;    

#Calculation
x=N*alpha_e/epsilon0;
epsilonr=(1+(2*x))/(1-x);     #dielectric constant(F/m)

#Result
print "dielectric constant is",round(epsilonr,3),"F/m"
print "answer in the book is wrong"

dielectric constant is 2.538 F/m
answer in the book is wrong

Example number 7.5, Page number 147

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

#Variable declaration
A=650*10**-4;      #area(m**2)
epsilon0=8.85*10**-12;    
d=4*10**-2;     #seperation(m)
Q=2*10**-10;    #charge(C)
epsilonr=3.5;   #dielectric constant

#Calculation
C=A*epsilon0/d;    
V=Q/C;    #voltage(V)

#Result
print "voltage is",round(V,1),"V"

voltage is 13.9 V

Example number 7.6, Page number 148

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

#Variable declaration
A=6.45*10**-4;      #area(m**2)
epsilon0=8.85*10**-12;    
d=2*10**-3;     #seperation(m)
epsilonr=5;   #dielectric constant
N=6.023*10**23;   #avagadro number

#Calculation
alpha_e=epsilon0*(epsilonr-1)/N;    #polarisability(Fm**2)

#Result
print "polarisability is",round(alpha_e*10**35,3),"*10**-35 Fm**2"
print "answer in the book is wrong"

polarisability is 5.877 *10**-35 Fm**2
answer in the book is wrong

Example number 7.7, Page number 148

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

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

#Calculation
r0=((epsilonr-1)/(4*math.pi*Na))**(1/3);     #radius of electron cloud(m)
X=x*E*r0**3/(Z*e);        #displacement(m)

#Result
print "radius of electron cloud is",round(r0*10**11,2),"*10**-11 m"
print "displacement is",round(X*10**17,4),"*10**-17 m"

radius of electron cloud is 5.86 *10**-11 m
displacement is 6.9999 *10**-17 m

Example number 7.8, Page number 149

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilonr=4;       #relative dielectric constant
Na=2.08*10**23;     #avagadro number
epsilon0=8.85*10**-12;    

#Calculation
x=(epsilonr-1)/(epsilonr+2);
alpha_e=x*3*epsilon0/Na;     #electronic polarisability(Fm**2)

#Result
print "electronic polarisability is",round(alpha_e*10**35,3),"*10**-35 Fm**2"
print "answer in the book is wrong"

electronic polarisability is 6.382 *10**-35 Fm**2
answer in the book is wrong

Example number 7.9, Page number 149

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
C=4*10**-6;    #capacitance(F)
epsilonr=200;       #relative dielectric constant
V=2000;       #voltage(V)

#Calculation
C0=C/epsilonr;    #energy in condenser(F)
E=C0*V/2;      #energy in dielectric(J)

#Result
print "energy in condenser is",C0,"F"
print "energy in dielectric is",E*10**4,"*10**-4 J"
print "answer in the book is wrong"

energy in condenser is 2e-08 F
energy in dielectric is 0.2 *10**-4 J
answer in the book is wrong

Example number 7.10, Page number 149

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

#Variable declaration
epsilon0=8.85*10**-12;    
N=2.7*10**25;   #density of atoms
R=0.55*10**-10;    #radius(m)

#Calculation
alpha_e=4*math.pi*epsilon0*R**3;     #polarisability(Fm**2)
epsilonr=(N*alpha_e/epsilon0)+1;     #relative permittivity

#Result
print "polarisability is",round(alpha_e*10**40,3),"*10**-40 Fm**2"
print "relative permittivity is",round(epsilonr,7),"Fm**2"

polarisability is 0.185 *10**-40 Fm**2
relative permittivity is 1.0000564 Fm**2

Example number 7.11, Page number 150

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

#Variable declaration
A=180*10**-4;     #area(m**2)
epsilonr=8;     #relative permittivity
C=3*10**-6;     #capacitance(F)
V=10;          #potential(V)
epsilon0=8.85*10**-12;    

#Calculation
E=V*C/(epsilon0*epsilonr);    #field strength(V/m)
dm=epsilon0*(epsilonr-1)*A*E;     #total dipole moment(coul m)

#Result
print "field strength is",round(E/10**6,4),"*10**6 V/m"
print "total dipole moment is",dm*10**6,"*10**-6 Coul. m"
print "answer in the book is wrong"

field strength is 0.4237 *10**6 V/m
total dipole moment is 0.4725 *10**-6 Coul. m
answer in the book is wrong