Chapter3:DIELECTRIC PROPERTIES OF MATERIALS

Eg1:pg-119

In [2]:
import math
Eg=6.0    #dielectric constant of glass plate
dg=0.25   #thickness of glass plate in mm
Ep=3.0    #dielectric constant of plastic film
dp=0.1    #thickness of plastic film in mm
Eo=8.85e-12 #permittivity of free space in F/m 
A=1       #let surface area be 1
Cg=Eg*Eo*A/dg
Cp=Ep*Eo*A/dp
ratio=Cg/Cp
print"Cg = ",ratio,"Cp"
print"Since Cp>Cg,the plastic film filled capacitor holds more charge than the glass plate filled capacitor"

Cg =  0.8 Cp
Since Cp>Cg,the plastic film filled capacitor holds more charge than the glass plate filled capacitor

Eg2:pg-120

In [3]:
import math
Er=2.8    #dielectric constant of a dielectric material
D=3e-8    #magnitude of electric displacement vector in C/m**2
p=(Er-1)*D/Er
print"Polarization is ",round(p,10),"C/m**2"

Polarization is  1.93e-08 C/m**2

Eg3:pg-120

In [4]:
import math
E=1000     #electric field in V/m
p=4.3e-8   #polarization in C/m**2
Eo=8.85e-12#permittivity of free space in F/m 
Er=1+(p/(Eo*E))
print"Relative permittivity of NaCl is ",round(Er,2)

Relative permittivity of NaCl is  5.86

Eg4:pg-120

In [6]:
import math
Er=1.000074  #dielectric constant of helium 
Eo=8.85e-12  #permittivity of free space in F/m (in book F/m2 is printed which is wrong)
E=100        #electric field in V/m
Na=6e23      #Avogadro number
V=22.4       #volume occupied by 1gm atom of gas at NTP in litres
N=Na/(V*1e-3)
p=Eo*(Er-1)*E
P=p/N
print"Induced dipole moment is ",round(P,42),"Cm"#answer in book is in different form as 24.42e-40 Cm

Induced dipole moment is  2.445e-39 Cm

Eg5:pg-121

In [8]:
import math
Epsilon=1.46e-10 #permittivity of diamond in C**2/Nm**2
Eo=8.86e-12      #permittivity of free space in C**2/Nm**2
Er=Epsilon/Eo    
X=Eo*(Er-1)
print"Dielectric constant is ",round(Er,2)
print"Electrical susceptibility is ",round(X,12),"C**2/Nm**2"

Dielectric constant is  16.48
Electrical susceptibility is  1.37e-10 C**2/Nm**2

Eg6:pg-121

In [10]:
import math
Xe=35.4e-12   #electrical susceptibility in C**2/Nm**2
Eo=8.85e-12   #permittivity of free space in C**2/Nm**2 
K=1+(Xe/Eo)
Epsilon=Eo*K
print"Dielectric constant is ",int(K)
print"Permittivity of the material is ",Epsilon,"C**2/Nm**2"
#answer in book is in different form as 44.25e-12 C**2/Nm**2

Dielectric constant is  5
Permittivity of the material is  4.425e-11 C**2/Nm**2

Eg7:pg-121

In [11]:
import math
Vo=60   #applied potential difference in volt
V=30    #reduced potential difference in volt
K=Vo/V
print"Dielectric constant of the liquid is ",K

Dielectric constant of the liquid is  2

Eg8:pg-121

In [12]:
import math
Vo=100   #potential difference in volts
t=0.3    #thickness of insulator in cm
A=100    #area in cm**2
d=1      #separation between plates in cm
K=7      #dielectric constant 
Eo=8.9e-12 #permittivity of free space in C**2/Nm**2
E_o=Vo/(d*1e-2)
E=E_o/K
D=K*Eo*E
p=(K-1)*Eo*E
print"E = ","{:.2e}".format(E),"Volt/m"
print"D = ",D,"C/m**2"
print"p = ",round(p,9),"C/m**2"

E =  1.43e+03 Volt/m
D =  8.9e-08 C/m**2
p =  7.6e-08 C/m**2

Eg9:pg-122

In [14]:
import math
E=6e4       #electric field in V/m
K=1.000134  #dielectric constant of neon
Eo=8.9e-12  #permittivity of free space in F/m
Na=6e23     #Avogadro number
V=22.4      #volume occupied by 1gm atom of gas at NTP in litres
p=Eo*(K-1)*E
N=Na/(V*1e-3)
P=p/N
alpha=P/(Eo*E)
print"Induced dipole moment is",round(P,38),"Cm"
print"Atomic polarizability of neon is ",round(alpha,32),"m**3"
#answer in book is wrong

Induced dipole moment is 2.67e-36 Cm
Atomic polarizability of neon is  5e-30 m**3

Eg11:pg-123

In [15]:
import math
Er=1.0024   #dielectric constant of argon atom
N=2.7e25    #number of atoms per cubic meter
Eo=8.85e-12 #permittivity of free space in F/m
alpha_e=Eo*(Er-1)/N
print"Electronic polarizability is ",round(alpha_e,41),"Fm**2"
#answer is wrong in book

Electronic polarizability is  7.9e-40 Fm**2

Eg12:pg-123

In [16]:
import math
N=9.8e26    #number of atoms in volume of one cubic meter of hydrogen gas
Eo=8.85e-12 #permittivity of free space in F/m
ao=0.53e-10 #radius of hydrogen atom in meter
alpha=4*math.pi*Eo*ao**3
Er=1+(4*math.pi*N*ao**3)
print"Polarizability is ",round(alpha,43),"Fm**2"
print"Relative permittivity is ",round(Er,4)

Polarizability is  1.66e-41 Fm**2
Relative permittivity is  1.0018

Eg13:pg-124

In [17]:
import math
alpha_300=2.5e-39 # total polarizability in C**2m/N at 300 K
alpha_400=2.0e-39 # total polarizability in C**2m/N at 400 K
T1 =300           # temperature in Kelvin
T2 =400           # temperature in Kelvin
beta=(alpha_300-alpha_400)*(T1*T2/(T2-T1))
alpha_def_300=alpha_300 - beta/300
alpha_oriant_300=beta/300
alpha_oriant_400=beta/400
print"Deformational Polarizability is ",alpha_def_300,"C**2mN**-1"
print"Orientational Polarizability at %d K is "%T1,alpha_oriant_300,"C**2mN**-1"
print"Orientational Polarizability at %d K is "%T2,alpha_oriant_400,"C**2mN**-1"

Deformational Polarizability is  5e-40 C**2mN**-1
Orientational Polarizability at 300 K is  2e-39 C**2mN**-1
Orientational Polarizability at 400 K is  1.5e-39 C**2mN**-1

Eg14:pg-132

In [18]:
import math
m=32              # Atomic weight of sulphur
d=2.08            # Density in g/cm**3
alpha_e=3.28e-40  # Electronic polarizability in Fm**2
Na=6.023e23       # Avogadro Number
Eo=8.85e-12       # Permittivity of free space in F/m
N=Na*d*1e6/m      
k=N*alpha_e/(3*Eo)
epsilon_r = (1+ k*2)/(1-k)# Calculation of relative permittivity
print"Relative dielectric constant is ",round(epsilon_r,1)

Relative dielectric constant is  3.8

Eg15:pg-132

In [19]:
import math
n=1.5  # Refractive index
Er=5.6 # Static dielectric constant
per=(1-((n**2-1)/(n**2+2))*(Er+2)/(Er-1))*100 # Pecentage of ionic polarizability
print"Percentage of ionic polarizability is ",round(per,1),"%"

Percentage of ionic polarizability is  51.4 %

Eg16:pg-133

In [20]:
import math
n=math.sqrt(2.69) # Refractive index
Er=4.94      # Static dielectric constant
k1=(Er-1)/(Er+2)
k2=(n**2-1)/(n**2+2)
ratio=1/round(((k1/k2)-1),3) 
print"Ratio of electronic to ionic polarizability is ",round(ratio,3)
#in book ai/ae is mentioned instead of ae/ai in final answer which is wrong

Ratio of electronic to ionic polarizability is  1.736

Eg17:pg-133

In [21]:
import math
Er=6.75  #dielectric constant of glass
n=1.5    #refractive index of glass
f=1e9    #frequency in Hz
per=(Er-n**2)*100/(Er-1)
print"Percentage attributed to ionic polarizability is ",round(per,1),"%"

Percentage attributed to ionic polarizability is  78.3 %

Eg18:pg-142

In [22]:
import math
t=5.5e-3    #thickness of quartz crystal plate in meter
p=2.65e3    #density of quartz crystal in Kg/m**3
Y=8e10      #Young's modulus of quartz in N/m**2 (value is wrong in question in book)
m=1         
f=m*math.sqrt(Y/p)/(2*t)
print"Frequency is ",int(f*1e-3),"KHz"

Frequency is  499 KHz

Eg19:pg-148

In [26]:
import math
import cmath
Er=4.36     #real part of dielectric constant of bakelite
N=4e28      #number of atoms per cubic meter
tan_d=2.8e-2#loss tangent at 1 MHz freuqency
Eo=8.853e-12#permittivity of free space in F/m
alpha=(3*Eo/N)*(Er*(1-(1j*tan_d))-1)/(Er*(1-(1j*tan_d))+2)
x=round(alpha.real*1e40,1)
y=round(alpha.imag*1e40,2)
alpha=complex(x,y)
print"Complex polarizability is ",alpha*1e-40,"Fm**2"
#in book answer is in different form and as (3.5-0.06i)*10**-40
#in book unit of answer is not mentioned

Complex polarizability is  (3.5e-40-6e-42j) Fm**2

Eg20:pg-149

In [27]:
import math 
t=18e-6   # Relaxation time in second
Er_d=1    # let real part of dielectric constant be 1
Er_dd=1   # let imaginary part of dielectric constant be 1
f=1/(2*math.pi*t) # Calculation of frequency
delta=math.atan(Er_dd/Er_d)
phi=90-(delta*180/math.pi) # Calculation of phase difference
print"Frequency is ",round(f/1e3,1),"KHz"
print"Phase difference between current and voltage is %d degree"%(phi)
print"Current leads the voltage "#this part is not mentioned in answer in book

Frequency is  8.8 KHz
Phase difference between current and voltage is 45 degree
Current leads the voltage