In [30]:

```
from math import *
from scipy import integrate
#Variable declaration
q = 1e-006; # Electric charge on either side of the dipole, C
l = 2e-02; # Dipole length, m
p = q*l; # Dipole moment for the pair of opposite charges, C-m
E = 1e+005; # External electric field, N/C
theta = 90; # Angle which the dipole makes with the external field, degrees
#Calculations&Results
tau = p*E*sin(theta); # The maximum torque on dipole placed in external electric field, Nm
print "The maximum torque = %1.0e N-m"%tau
W = p*E*(cos(0)-cos(180*pi/180))
#W = integrate('p*E*sin(thet)', 'thet', 0, pi); # The work done in rotating the dipole direction = %1.0e J", W
print "The work done in rotating the dipole direction = %1.0e J"%W
```

In [2]:

```
from math import *
#Variable declaration
Q = 8e-019; # Charge of the nucleus, C
p = 3.2e-029; # Electric dipole moment, C-m
r = 1e-10; # Distance of dipole relative to the nucleus, m
k = 9e+9; # Coulomb constant, N-meter-square/C-square
theta = 0; # Angle for radial direction, radian
#Calculations&Results
F = k*p*Q*sqrt(3*cos(theta**2)+1)/r**3; # The force acting on the dipole in the radial direction, N
print "The force acting on the dipole in the radial direction = %3.1e N"%F
theta = pi/2; # Angle for perpendicular direction, radian
F = k*p*Q*sqrt(3*cos(theta)**2+1)/r**3;
print "The force acting on the dipole in the direction perpendicular to radial direction = %3.1e N"%F
```

In [3]:

```
#Variable declaration
chi_e = 35.4e-12; # Susceptability of the material, C-square/N-meter-square
eps_0 = 8.85e-12; # Electric permittivity in free space, C-squre/N-meter-square
#Calculations&Results
K = 1 + (chi_e/eps_0);
print "The dielectric constant = %d "%K
eps = (eps_0*K);
print "The electric permittivity = %5.3e C-square/N-meter square "%eps
```

In [4]:

```
#Variable declaration
eps = 1.46e-10; # Electric permittivity, C-square/n-meter-square
eps_0 = 8.85e-12; # Permittivity in free space, C-squre/N-meter-square
#Calculations&Results
K = (eps/eps_0);
print "The dielectric constant = %4.1f "%K
chi_e = eps_0*(K-1); # Susceptability,in C-square/N-meter-square
print "The electric susceptability = %4.2e C-square/N-meter square "%chi_e
```

In [5]:

```
#Variable declaration
K = 7.0; # Dielectric constant of the slab
d = 0.01; # Distance between the two parallel plates, m
V_0 = 100; # Potential difference across the plates, V
eps_0 = 8.85e-12; # Electric permability of the free space, C-square/N-meter-square
#Calculations&Results
E_0 = V_0/d; # Electric intensity in the absence of dielectric slab, V/m
E = E_0/K; # Electric intensity with dielectric slab introduced between the plates, V/m
print "The electric field intensity in the presence of the dielectric slab = %4.2e V/m "%E
D = (eps_0*K*E); # Electric displacement, C-square/m-square
print "The electric displacement in the dielectric slab = %4.2e C-square/meter-square "%D
P = eps_0*(K-1)*E; # Electric polarization in the dielectric slab, C-square/m-square
print "The electric polarization in the dielectric slab = %3.1e C-square/meter-square "%P
```

In [6]:

```
#Variable declaration
K = 1.000074; # Dielectric constant of the He
n = 2.69e+025; # Atomic density of He, atoms/meter-cube
eps_0 = 8.85e-012; # Electric permability of the free space, C-square/N-meter-square
E = 1; # Electric field strength, V/m
#Calculations
p = (eps_0*(K-1)*E)/n; # Dipole moment induced in He, C-m
#Result
print "The dipole moment induced in each He atom = %4.2e C-m "%p
```

In [7]:

```
#Variable declaration
K = 1.000134; # Dielectric constant of the neon
n = 2.69e+25; # Atomic density of argon,atoms/meter-cube
eps_0 = 8.85e-12; # Electric Permability in the free space, C-square/N-meter-square
E = 90e+03; # External electric field, V/m
#Calculations
p = eps_0*(K-1)*E/n; # Dipole moment induced in each neon atom, C-m
alpha = p/E; # Atomic polarizability of neon gas, C-metre-square/V
#Results
print "The induced dipole moment of noen atom = %4.2e C-m"%p
print "The electronic polarizability of neon gas = %3.1e C-m-square/V "%alpha
```

In [8]:

```
#Variable declaration
K = 1.0024; # Dielectric constant of the argon
n = 2.7e+25; # Atomic density of argon,atoms/meter-cube
eps_0 = 8.85e-12; # Electric Permability in the free space, C-square/N-meter-square
#Calculations
alpha = eps_0*(K-1)/n;
#Result
print "The electronic polarizability of argon atom = %4.1e C-m-square/V "%alpha
```

In [9]:

```
#Variable declaration
K = 2.24; # Dielectric constant
eps_0 = 8.85e-12; # Electric permability in the free space, C-square/N-meter-square
rho = 1.6e+003; # Density of CCl4, kg/meter-cube
M = 156; # Molecular weight of CCl4
E = 1e+007; # External electric field strength, V/m
N_A = 6.02e+26; # Avogadro's number, per kmol
#Calculations
rho_M = rho*N_A/M; # Molecular density of CCl4
p = eps_0*(K-1)*E/rho_M; # Individual dipole moment of CCL4 molecule, C-m
#Result
print "Individual dipole moment of CCL4 molecule = %4.2e C-m "%p
```

In [11]:

```
from math import *
#Variable declaration
K = 1.0000684; # Dielectric constant of He at 1 atm
n = 2.7e+25; # Density of He at 1 atm and 273 K, atoms/meter-cube
#Calculations
# The atomic polarizibility, alpha = eps_0*(K-1)/n
# In terms of atomic radius, alpha = 4*%pi*eps_0*R^3 so, we have
R = ((K-1)/(4*pi*n))**(1./3); # Radius of He atom, m
#Result
print "The atomic radius of He = %4.2e m "%R
```

In [12]:

```
#Variable declaration
mu = 1.5; # Optical index of refraction of NaCl crystal
K = 5.6; # Static dielectric constant of NaCl crystal
#Calculations
P_IP = (1-((mu**2-1)*(K+2))/((mu**2+2)*(K-1)))*100;
#Result
print "The percentage of ionic polarizibility in NaCl crystal = %4.1f percent "%P_IP
```

In [31]:

```
from math import *
#Variable declaration
K_B = 1.38e-23; # Boltzmann constant, J/mol/K
T = 300; # Room temperature, K
eps_0 = 8.85e-12; # Electric permittivity of free space, F/m
N_A = 6.0e+23; # Avogadro's number
#Calculations
n2 = N_A*1000; # Number of molecules of non-polar substance in 1000 cc volume
p_0 = sqrt((9*K_B*T*eps_0*0.023)/n2); # Dipole moment of polar molecules, C-m
#Result
print "The dipole moment of polar molecules = %4.3e C-m"%p_0
```