Chapter 7: Dielectric Properties

Example 7.1, Page number 7.23

In [1]:
#Variable declaration
C = 2*10**-6   #Capacitance(F)
V = 1000       #voltage(V)
Er = 100       #permittivity

#Calculations
W = (C*V**2)/2

Co = C/Er
Wo = (Co*V**2)/2
Wf = W-Wo

#Result
print "Energy stored in condenser =",W,"J"
print "Energy stored in polarizing the dilectric =",Wf,"J"

Energy stored in condenser = 1.0 J
Energy stored in polarizing the dilectric = 0.99 J

Example 7.2, Page number 7.24

In [5]:
#Variable declaraion
Er = 4.94   #permittivity
n2 = 2.69   #index of refraction

#Calculations
'''
Er - 1    N(ae+ai)
------ = ---------
Er + 2     3*Eo 
Sunbstituting the values for Er, we get,
N(ae+ai)       
--------  = 0.5677           ------------(1)
  3*ao
'''
x = 0.5677

'''
Also, Er = n**2
Therefore, n**2-1    N*ae
           ------- = -----
            n**2+2    3*Eo
Substituting the values for n^2, we get,
N*ae
---- = 0.36034   ---------------(2)
3*Eo
'''
y = 0.36034
#Let z = ai/ae
#Dividing equation (1) by (2), we get,

z = (x/y)-1

#Result
print "Ratio between electronic and ionic probabbility is",round(z,3) ,"or",round((1/z),3)

Ratio between electronic and ionic probabbility is 0.575 or 1.738

Example 7.3, Page number 7.25

In [6]:
import math

#Variable declaration
Er = 2.56         #permittivity
f = 1*10**6       #frequency(Hz)
A = 8*10**-4      #area(m^2)
d= 0.08*10**-3    #distance of seperation(m)
Eo = 8.85*10**-12

#Calculations
Er_dash = Er*0.7*10**-4
w = 2*math.pi*f
Rp = d/(w*Eo*Er_dash*A)

Cp = (A*Eo*Er)/d

#Results
print "Parallel loss resistance =",round((Rp/1E+6),2),"MOhms"
print "Capacitance =",Cp,"F(Calculation mistake in textbook)"

Parallel loss resistance = 10.04 MOhms
Capacitance = 2.2656e-10 F(Calculation mistake in textbook)

Example 7.5, Page number 7.26

In [7]:
#Varaible declaration
N = 3.*10**28       #density(atoms/m^3)
ae = 10.**-40       #electronic polarizability(F m^2)
Eo = 8.854*10**-12  #permittivity of free space(F/m)

#Calculaion
Er = 1+((N*ae)/Eo)

#Result
print "dielectric constant =",round(Er,3)

dielectric constant = 1.339

Example 7.5, Page number 7.26

In [8]:
#Variable declaration
Er = 1.0000684      #permittivity of dilectric
Eo = 8.854*10**-12  #permittivity of free space(F/m)
N = 2.7*10**25      #density(atoms/m^3)

#Calculation
ae = (Eo*(Er-1))/N

#Result
print "Electronic polarizability =",round((ae/1E-41),3),"*10^-41 Fm^2"

Electronic polarizability = 2.243 *10^-41 Fm^2

Example 7.6, Page number 7.27

In [10]:
#Variable declaration
A = 100*10**-4      #area of parallel capacitor(m^2)
d = 1*10**-2        #separation between plates(m)
Eo = 8.854*10**-12  #permittivity of free space(F/m)
V = 100             #voltage(V)

#Calculation
C = (Eo*A)/d
Q = C*V

#Result
print "Capacitance =",round((C/1E-12),2),"pF"
print "Charge =",Q,"C"

Capacitance = 8.85 pF
Charge = 8.854e-10 C

Example 7.7, Page number 7.28

In [11]:
#Variable declaration
N = 6.02*10**26    #Avogadro's number
den = 2050         #density(kg/m^3)
Ma = 32            #atomic weight
Eo = 8.55*10**-12 #permittivity of free space(F/m)
v = 1/3            #internal field constant
Er = 3.75          #dielectric constant of sulphur

#Calculations
n = (N*den)/Ma     #no. of atoms per m^3
ae = ((Er-1)/(Er+2))*((3*Eo)/n)

#Result
print "Electronic polarizability =",round((ae/1E-40),3),"*10^-41 Fm^2"

Electronic polarizability = 3.181 *10^-41 Fm^2