6: Dielectric properties

Example number 6.1, Page number 6.23

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
N=3*10**28;     #number of atoms(per m**3)
alpha_e=10**-40;    #electronic polarizability(F m**2)
epsilon0=8.85*10**-12;     

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

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

dielectric constant of material is 1.339

Example number 6.2, Page number 6.24

In [35]:
#importing modules
import math
from __future__ import division

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

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

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

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

Example number 6.3, Page number 6.24

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;
epsilonr=1.0000684;      #dielectric constant of material
N=2.7*10**25;    #number of atoms(per m**3)

#Calculation
alpha_e=epsilon0*(epsilonr-1)/N;     #electronic polarizability(F m**2)

#Result
print "electronic polarizability is",alpha_e,"F m**2"

electronic polarizability is 2.242e-41 F m**2

Example number 6.4, Page number 6.24

In [38]:
#importing modules
import math
from __future__ import division

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

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

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

voltage is 39.73 V

Example number 6.5, Page number 6.25

In [39]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;
A=6.45*10**-4;     #area(m**2)
d=2*10**-3;     #seperation(m)
V=12;    #voltage(V)
epsilonr=5;

#Calculation
P=epsilon0*(epsilonr-1)*V/d;     #polarization(C m)

#Result
print "polarization is",P*10**9,"*10**-9 C m"

polarization is 212.4 *10**-9 C m

Example number 6.6, Page number 6.25

In [40]:
#importing modules
import math
from __future__ import division

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

#Calculation
N=Na*D/M;     #number of atoms(per m**3)
alphae=((epsilonr-1)/(epsilonr+2))*3*epsilon0/N;    #electronic polarizability(F m**2)

#Result
print "electronic polarizability is",round(alphae*10**40,2),"*10**-40 F m**2"
print "answer varies due to rounding off errors"

electronic polarizability is 3.29 *10**-40 F m**2
answer varies due to rounding off errors

Example number 6.7, Page number 6.26

In [43]:
#importing modules
import math
from __future__ import division

#Variable declaration
N=1.6*10**20;     #number of molecules(/m**3)
T=300;     #temperature(K)
E=5*10**5;    #electric field(V/m)
x=0.25*10**-9;   #separation(m)
Kb=1.381*10**-23;    #boltzmann constant
e=1.6*10**-19;  

#Calculation
Pd=N*e**2*x**2*E/(3*Kb*T);      #orientational polarization

#Result
print "orientational polarization is",round(Pd*10**11,4),"*10**-11 C m"

orientational polarization is 1.0298 *10**-11 C m

Example number 6.8, Page number 6.26

In [51]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;
epsilonr=1.0000684;      #dielectric constant of material
N=2.7*10**25;    #number of atoms(per m**3)
E=10**6;     #electric field(V/m)
e=1.6*10**-19;  
Z=2;     #atomic number

#Calculation
alpha_e=epsilon0*(epsilonr-1)/N;     #electronic polarizability(F m**2)
r=(alpha_e/(4*math.pi*epsilon0))**(1/3);     #radius(m)
d=alpha_e*E/(Z*e);     #displacement(m)

#Result
print "radius is",round(r*10**11,3),"*10**-11 m"
print "answer varies due to rounding off errors"
print "displacement is",round(d*10**16,1),"*10**-16 m"

radius is 5.864 *10**-11 m
answer varies due to rounding off errors
displacement is 0.7 *10**-16 m

Example number 6.9, Page number 6.27

In [54]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;
A=750*10**-6;     #area(m**2)
d=5*10**-3;     #seperation(m)
Q=2.5*10**-10;    #charge(C)
epsilonr=3.5;

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

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

voltage is 53.8 V

Example number 6.10, Page number 6.27

In [55]:
#importing modules
import math
from __future__ import division

#Variable declaration
N=3*10**25;    #number of atoms(per m**3)
r=0.2*10**-9;    #radius(m)
epsilon0=8.85*10**-12;
E=1;     #electric field

#Calculation
p=4*math.pi*epsilon0*r**3;    #dipole moment(F m**2)
P=N*p;     #polarization(C m)
epsilonr=(P/(epsilon0*E))+1;     #dielectric constant
alpha_e=epsilon0*(epsilonr-1)/N;    #polarizability(F m**2)

#Result
print "dipole moment is",round(p*10**40,1),"*10**-40 F m**2"
print "polarization is",round(P*10**15,1),"*10**-15 C m"
print "dielectric constant is",round(epsilonr,5)
print "polarizability is",round(alpha_e*10**40,1),"*10**-40 F m**2"

dipole moment is 8.9 *10**-40 F m**2
polarization is 26.7 *10**-15 C m
dielectric constant is 1.00302
polarizability is 8.9 *10**-40 F m**2

Example number 6.11, Page number 6.28

In [57]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;
epsilonr=1.000435;      #dielectric constant of material
N=2.7*10**25;    #number of atoms(per m**3)

#Calculation
alpha_e=epsilon0*(epsilonr-1)/N;     #electronic polarizability(F m**2)

#Result
print "electronic polarizability is",round(alpha_e*10**40,3),"*10**-40 F m**2"

electronic polarizability is 1.426 *10**-40 F m**2

Example number 6.12, Page number 6.28

In [63]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.85*10**-12;
epsilonr=4;    #dielectric constant
D=2.08*10**3;    #density(kg/m**3)
Na=6.02*10**26;    #avagadro number
M=32;    #atomic weight

#Calculation
N=Na*D/M;     #number of atoms(per m**3)
alphae=epsilon0*(epsilonr-1)/N;    #atomic polarizability(F m**2)

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

electronic polarizability is 6.785 *10**-40 F m**2