10: Dielectric properties

Example number 10.1, Page number 10.23

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

#Variable declaration
C=2*10**-6;    #capacitance(F)
V=1000;      #voltage(V)
epsilon_r=100;

#Calculation
W=C*V**2/2;    #energy stored in the condenser(J)
C0=C/epsilon_r;
W0=C0*V**2/2;
E=1-W0;       #energy stored in the dielectric(J)

#Result
print "energy stored in the condenser is",W,"J"
print "energy stored in the dielectric is",E,"J"

energy stored in the condenser is 1.0 J
energy stored in the dielectric is 0.99 J

Example number 10.2, Page number 10.24

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

#Variable declaration
epsilon_r=4.94;
n2=2.69;

#Calculation
x=(epsilon_r-1)/(epsilon_r+2);
y=(n2-1)/(n2+2);
r=(x/y)-1;       #ratio betwen electronic and ionic polarizability

#Result
print "ratio betwen electronic and ionic polarizability is",round(1/r,3)

ratio betwen electronic and ionic polarizability is 1.738

Example number 10.3, Page number 10.24

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

#Variable declaration
epsilon_r=2.56;
epsilon_R=2.65*0.7*10**-4;
tan_delta=0.7*10**-4;   
A=8*10**-4;    #area(m**2)
d=0.08*10**-3;    #diameter(m)
f=1*10**6;    #frequency(Hz)
epsilon0=8.85*10**-12;

#Calculation
Rp=d/(2*math.pi*f*epsilon0*epsilon_R*A);    #parallel loss resistance(ohm)
Cp=A*epsilon0*epsilon_r/d;     #parallel loss capacitance(Farad)

#Result
print "parallel loss resistance is",round(Rp/10**6),"ohm"
print "answer varies due to rounding off errors"
print "parallel loss capacitance is",round(Cp*10**12,2),"*10**-12 Farad"

parallel loss resistance is 10.0 ohm
answer varies due to rounding off errors
parallel loss capacitance is 226.56 *10**-12 Farad

Example number 10.4, Page number 10.25

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

#Variable declaration
N=3*10**28;     #number of atoms(per m**3)
alphae=10**-40;    
epsilon0=8.854*10**-12;

#Calculation
epsilon_r=1+(N*alphae/epsilon0);   #dielectric constant of material

#Result
print "dielectric constant of material is",round(epsilon_r,3)

dielectric constant of material is 1.339

Example number 10.5, Page number 10.26

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

#Variable declaration
N=2.7*10**25;     #number of atoms(per m**3)
epsilon0=8.854*10**-12;
epsilon_r=1.0000684;

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

#Result
print "electronic polarizability is",round(alphae*10**41,3),"*10**-41 Fm**2"

electronic polarizability is 2.243 *10**-41 Fm**2

Example number 10.6, Page number 10.26

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

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

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

#Result
print "capacitance is",C,"F"
print "charge on plates is",Q,"coulomb"

capacitance is 8.85e-12 F
charge on plates is 8.85e-10 coulomb

Example number 10.7, Page number 10.27

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

#Variable declaration
n=6.02*10**26;     #avagadro number
d=2050;     #density(kg/m**3)
w=32;       #atomic weight
gama=1/3;    #internal field constant
epsilon0=8.55*10**-12;
epsilon_r=3.75;

#Calculation
N=n*d/w;       #number of atoms(per m**3)
alphae=3*epsilon0*((epsilon_r-1)/(epsilon_r+2))/N;      #electronic polarizability(Fm**2)

#Result
print "electronic polarizability is",round(alphae*10**40,3),"*10**-40 Fm**2"

electronic polarizability is 3.181 *10**-40 Fm**2

Example number 10.8, Page number 10.28

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

#Variable declaration
Q=2*10**-10;    #charge(C)
d=4*10**-3;     #seperation(m)
epsilon_r=3.5;
A=650*10**-6;    #area(m**2)
epsilon0=8.85*10**-12;

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

#Result
print "resultant voltage is",round(V,2),"Volts"

resultant voltage is 39.73 Volts

Example number 10.9, Page number 10.28

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=2*10**-3;     #seperation(m)
epsilon_r=6;
V=10;      #voltage(V)
epsilon0=8.85*10**-12;

#Calculation
E=V/d;
D=epsilon0*epsilon_r*E;      #dielectric displacement(C m**-2)

#Result
print "dielectric displacement is",round(D*10**9,1),"*10**-9 C m**-2"

dielectric displacement is 265.5 *10**-9 C m**-2