import math
alpha = 1.8*10**-40; #polarisability of argon in Fm**2
e0 = 8.85*10**-12; #dielectric constant F/m
N1 = 6.02*10**23; #avagadro number in mol**-1
x = 22.4*10**3; #volume in m**3
#formula
#er-1=N*p/e0*E=(N/e0)*alpha
#calculation
N = N1/float(x); #number of argon atoms in per unit volume in cm**3
N2 = N*10**6; #number of argon atoms in per unit volume in m**3
er = 1+((N2/float(e0)))*(alpha); #dielectric constant F/m
#result
print'dielectric constant of argon = %3.7f'%er;
import math
#variable declaration
alpha = 1.8*10**-40; #polarisability of argon in F*m^2
E = 2*10**5; # in V/m
z = 18;
e = 1.6*10**-19;
#formula
#p=18*e*x
#calculation
p = alpha*E;
x = p/float(18*e); #displacement in m
#result
print'displacement = %3.2e'%x,'m';
import math
#variable declaration
E0 = 300*10**2; #local field in V/m
P1 = 3.398*10**-7; #dipole moment Coulomb/m
P2 = 2.124*10**-5; #dipole moment Coulomb/m
e0 = 8.85*10**-12; #permittivity in F/m
#formula
#E10Ci=E0-(2*Pi/3*e0)
#calculation
E10C1 = E0-((2*P1)/float(3*e0)); #local field of benzene in V/m
E10C2 = E0-((2*P2)/float(3*e0)); #local field of water in V/m
#result
print'local field of benzene=%3.2e'%E10C1,'V/m';
print'local field of water=%3.3e'%E10C2,'V/m';
import math
#variable declaration
p1 = 5.12*10**-34; #p of benzene kg/m**3
p2 = 6.34*10**-34; #p of water kg/m**3
e10C1 = 4.4*10**3; #local field of benzene in V/m
e10C2 = 1570*10**3; #local field of water in V/m
#formula
#p=alphai*e10Ci
#calculation
alpha1 = p1/float(e10C1); #polarisability of benzene in F*m**2
alpha2 = p2/float(e10C2); #polarisability of water in F*m**2
#result
print'polarisability of benzene = %3.2e'%alpha1,'F*m**2';
print'polarisability of water = %3.2e'%alpha2,'F*m**2';
print'Note: mistake in textbok,alpha1 value is printed as 1.16*10**-38 instead of 1.16*10**-37';
import math
#variable declaration
e0 = 8.85*10**-12; #abslute permitivity in (m**-3)*(kg**-1)*(s**4)*(A**2)
E = 600*10**2; #strength in V/cm
er1 = 2.28; #dielectric constant of benzene in coulomb/m
er2 = 81; #dielectric constant of water in coulomb/m
#fomula
#p=e0*E*(er-1)
#calculation
pB = e0*E*(er1-1); #polarisation of benzene in c/m**2
pW = e0*E*(er2-1); #polarisation of water in c/m**2
#result
print'polarisation of benzene = %3.2e'%pB,'c/m**2';
print'polarisation of water = %3.2e.'%pW,'c/m**2';
import math
#variable declaration
er0 = 5.6; #static dielectric cnstant of NaCl
n = 1.5; #optical index of refraction
#calculation
er = er0-n**2;
d = ((er/float(er0))*100); #percentage contribution from ionic polaristion in %
#result
print'percentage contribution from ionic polaristion = %3.2f'%d,'%';
import math
#variable declaration
alpha = 0.18*10**-40; #polarisability of He in F *m**2
E = 3*10**5; #constant in V/m
N = 2.6*10**25; #number of atoms in per m**3
e = 1.6*10**-19;
#formula
#P=N*p
#charge of He=2*electron charge
#p=2(e*d)
#calculation
P = N*alpha*E; #in coul/m**2
p = P/float(N); #polarisation of He in coul.m
d = p/float(2*e); #separation between charges in m
#result
print'separation=%3.2e'%d,'m';
import math
#variable declaration
N = 10**27; #number of HCl molecules in molecules/m**3
E = 10**5; #electric field in V/m
P = 1.04*3.33*10**-30; #permanent dipole moment in coul.m
T = 300; #temperature in kelvin
K = 1.38*10**-23;
#calculation
P0 = (N*(P**2)*E)/float(3*K*T); #oriental polarisation in coul/m^2
#result
print'oriental polarisation=%3.2e'%P0,'coul/m**2';
import math
#variable declaration
N = 6.023*10**26; #avagadro number (lb-mol)**-1
alpha = 3.28*10**-40; #polarisability in F*m**2
M = 32; #molecular weight in kilograms
p = 2.08*10**3; #density of sulphur in g/cm**3
e0 = 8.85*10**12; #permitivity in F/m
#calculation
er = ((2*N*p*alpha)+(3*M*e0))/float((3*M*e0)-(N*p*alpha));
#result
print'relative dielectric constant =%3.1f'%er;
print' Note: calculation mistake in text book in calculating relative dielectric constant';
import math
#variable declaration
er = 4.94;
n = 1.64;
#calculation
#(alphae)/(alphai) =x
x = ((er-1)/float(er+2))*(((n**2)+2)/float((n**2)-1)); #ratio of electronic and ionic probabilities
#result
print'ratio of electronic and ionic probabilities =%3.1f'%x;
import math
#variable declartion
E = 1.46*10**-10; #permitivity in c**2*N**-1*m**-2
E0 = 8.885*10**-12; #permitivity in c**2*N**-1*m**-2
#calculation
Er = E/float(E0);
sighe = E0*(Er-1); #electrical susceptbility in c**2*N**-1*M**-2
#result
print'dielectric constant=%3.2f'%Er;
print'electrical suseptibility=%3.4e'%sighe,'c**2*N**-1*M**-2';
import math
#variable declaration
r = 0.1; #radius in m
pw = 1; #density of water in g/ml
Mw = 18; # molecular mass of water
E = 6.0*10**-30; #dipole moment of water in cm
N = 6.0*10**26; #avagadro constant in (lb-mol)−1
#calculation
n = N*(4*(math.pi)*(r**3)*pw)/(Mw*3); #number of water molecules in a water drop
p = n*E; #polarisation in cm**2
#result
print'polarisation=%3.1e'%p,'cm**2';
import math
#variable declaration
Er = 1.000074; #dielectric constant for a gas at 0°C
#calculation
sighe = Er-1; #dielectric susceptibility
#result
print'dielectric susceptibility=%3.6f'%sighe;
import math
#variable declaration
E = 10**6; #dielectric in volts/s
er = 3; #dielectric in mm
e0 = 8.85*10**-12;
#calculation
E0 = er*E; #electric field in V/m
sigma = e0*E0; #free charge in Coul/m^2
P = e0*(er-1)*E0; #polarisation in coul/m
D = e0*er*E0; #displacement in in dielectric
#result
print'free charge=%3.2e'%sigma,'Coul/m**2';
print'polarisation=%3.2e'%P,'Coul/m';
print'displacement=%3.2e'%D;
import math
#variable declaration
d = 1.0*10**-3; #separation between plates in m
A = 6.45*10**-4; # surface area in m^2
e0 = 8.85*10**-12; #permitivity of electron in (m**-3)*(kg**-1)*(s**4)*(A**2)
er = 6.0; #relative permitivity in (m**-3)*(kg**-1)*(s**4)*(A**2)
V = 10; #voltage in V
E = 10;
#calculation
C = (e0*er*A)/float(d); #capacitance in Farad
q = C*V; #charge in coulomb
D = (e0*er*E)/float(10**-3); #displacement vector in c/m**2
P = D-(e0*E/float(10**-3)); #polarisation vector in c/m**2
#result
print'capacitance = %3.2e'%C,'Farad';
print'charge =%3.2e'%q,'coulomb';
print'displacement =%3.2e'%D,'c/m**2';
print'polarisation =%3.2e'%P,'c/m**2';
print'Note:error in calculation of P,E value is taken as 5000 instead of 10**4\n';
import math
#variable declaration
t = 18*10**-6; #relaxation time in s
er1 = 1; #permitivity in F/m
er = 1; #permitivity in F/m
t = 18*10**-6; #relaxation time in s
#calculation
f = 1/float(2*math.pi*t); #frequency in Hz
theta_c = math.atan(er1/float(er));
#theta_c_deg = (theta_c*180)/float(math.pi);
#phi = 90-theta_c_deg; #phase difference in degrees
#result
print'frequency = %3.2f'%(f*10**-3),'KHz';
print'phase difference =%3.0f'%((theta_c*180)/float(math.pi)),'°';