In [1]:

```
from __future__ import division
import numpy as np
from math import pi
#variable delaration
mu_0 = 4*pi*10**(-7) # permeability in free space
mu_r1 = 3 # region 1 relative permeability
mu_r2 = 5 # region 2 relative permeability
mu_1 = mu_r1*mu_0 # region 1 permeability
mu_2 = mu_r2*mu_0 # region 2 permeability
#calculations
H1 = np.array([4,1.5,-3]) # magnetic field in region 1 in A/m
Ht1 = np.array([0,1.5,-3]) # tangential component of magnetic field H1
Hn1 = np.array([4,0,0]) # normal component of magnetic field H1
Ht2 = np.array([0,1.5,-3]) # as tangential componenet of magnetic field H2 = tangential component of magnetic field H1
Hn2 = (mu_1/mu_2)*Hn1 # normal component of magnetic field H2
H2 = Ht2+Hn2 # magnetic field in region 2 in A/m
h2 = np.linalg.norm(H2) # magnitude of the magnetic field H2 in A/m
#results
print "magnetic field in region 2 in A/m:",np.around(H2,2)
print "magnitude of magnetic field in region 2 in A/m:",round(h2,3)
```

In [21]:

```
from __future__ import division
import numpy as np
#variable Declaration
epsilon_0 = 8.854*10**(-12) # permittivity in free space
sigma_1 = 0 #conductivity of medium 1
sigma_2 = 0 #conductivity of medium 2
epsilon_r1 = 1 # region 1 relative permittivity
epsilon_r2 = 2 # region 2 relative permittivity
#calculations
epsilon_1 = epsilon_r1*epsilon_0 # region 1 permittivity
epsilon_2 = epsilon_r2*epsilon_0 # region 2 permittivity
E1 = np.array([1,2,3]) # Electric field in region 1 in V/m
Et1 = np.array([0,2,3]) # tangential component of electric field E1
En1 = np.array([1,0,0]) # normal component of electric field E1
Et2 = np.array([0,2,3]) # as tangential componenet of electric field E2 = tangential component of electric field E1
En2 = (epsilon_1/epsilon_2)*En1 # normal component of electric field E2
E2 = Et2+En2 # electric field in region 2 in V/m
Dt1 = epsilon_0*Et1 # tangential component of electric flux density D1
D2 = epsilon_2*E2 # electric flux density in region 2 in C/m**2
#Results
print "electric field in region 2 in V/m:",np.around(E2,2)
print "electric flux density in region 2 in C/m**2:",D2
```

In [3]:

```
from __future__ import division
import numpy as np
from math import pi
#variable Declaration
# H = cos(10**8*t-Beta*z)ay # magnetic field in A/m
# E = 377*cos(10**8*t-Beta*z)ax # electric field in V/m
omega = 10**8 # angular frequency in Hz
v_0 = 3*10**8 # speed of light in m/s
#calculations
f = omega/(2*pi) # frequency in Hz
lamda = v_0/f # wavelength in m
Beta = (2*pi)/lamda # phase constant in rad/m
print "eta_0 = E/H = 377*cos(10**8*t-Beta*z)/cos(10**8*t-Beta*z) = > E/H = 377"
eta_0 = abs(377) # intrinsic impedence in ohm
#Results
print "intrinsic impedence in ohm:",eta_0
print "frequency in MHz:",round(f/(10**6),3)
print "phase constant in rad/m:",round(Beta,3)
print "wavelength in m:",round(lamda,3)
```

In [22]:

```
from __future__ import division
from math import pi
import numpy as np
#Variable Declaration
f = 100 # frequency in MHz
f = 100*10**6 # frequency in Hz
v_0=3*10**8 # speed of light in m/s
# formula : Gamma = omega(j)*sqrt(mu_0*epsilon_0)=omega(j)/v_0 =(2j*pi*f)/v_0
Gamma =(2j*pi*f)/(v_0) # propagation constant
#result
print "propagation constant in m**-1:",np.around(Gamma,3)
```

In [5]:

```
from __future__ import division
from math import pi
#Variable Declaration
# H(z,t) = 48*cos(10**8*t+40*z)ay # equation of magnetic field
A = 48 # amplitude of the magnetic field in A/m
omega = 10**8 # angular frequency in radians/sec
Beta = 40 # phase constant in rad/m
#Calculations
f = omega/(2*pi) # frequency in Hz
lamda = (2*pi)/Beta # wavelength in m
#results
print "amplitude of the magnetic field in A/m:",A
print "frequency in MHz:",round(f/10**6,3)
print "phase constant in rad/m:",round(Beta,3)
print "wavelength in m:",round(lamda,3)
```

In [6]:

```
from __future__ import division
from math import pi,sqrt
#Variable Declaration
H = 2 # ampliutude of magnetic field in A/m
sigma = 0 # conductivity
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
#calculations
mu = mu_0 # permeability in F/m
epsilon = 4*epsilon_0 # permittivity in F/m
Eta_0 = 120*pi # intrinsic impedence in free space in ohm
E_free = Eta_0*H # electric field in V/m
#results
print "magnitude of electric field in V/m in free space:",round(E_free,3)
Eta = sqrt(mu/epsilon) # intrinsic impedence in ohm
E = Eta*H # magnitude of electric field
print "magnitude of electric field in V/m:",round(E,3)
```

In [23]:

```
from __future__ import division
from math import pi,sqrt
import numpy as np
#variable Declaration
sigma = 0 # conductivity in mho/m
f = 0.3 # frequency in GHz
f = 0.3*10**9 # frequency in Hz
omega = 2*pi*f # angular frequency in rad/sec
# formula : Gamma = sqrt(1j*omega*mu*(sigma+1j*omega*epsilon)) = 1j*omega*sqrt(mu*epsilon)
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
epsilon = 9*epsilon_0 # permittivity in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
mu = mu_0 # permeability in H/m
Gamma = 1j*omega*sqrt(mu*epsilon) # propagation constant im m**-1
#results
print "propagation constant im m**-1:",np.around(Gamma,3)
# formula : eta = sqrt((1j*omega*mu)/(sigma+omega*epsilon)) = sqrt(mu/epsilon)
eta = sqrt(mu_0/(9*epsilon_0)) # intrinsic impedence in ohm
print "intrinsic impedence in ohm:",round(eta,3)
# note : answer in the book is wrong.
```

In [8]:

```
from __future__ import division
from math import sqrt,pi
#variable declaration
lamda = 0.25 # wavelength in m
v = 1.5*10**10 # velocity of propagation of wave in cm/sec
v = 1.5*10**8 # velocity of propagation of wave in m/sec
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
mu = mu_0 # permeability in H/m
v_0 = 3*10**8 # speed of light in m/s
f = v/lamda # frequency in Hz
# formula : v = 1/(mu*epsilon) = 1/(mu_0*epsilon_0*epsilon_r) = v_0/sqrt(epsilon_r)
epsilon_r = (v_0/v)**2 # relative permittivity
#results
print "frequecy in MHz:",round(f/10**6,3)
print "relative permittivity:",epsilon_r
# note : answer in the book is wrong.
```

In [9]:

```
from __future__ import division
from math import sqrt,pi
#variable declaration and calculations
#E = 5*sin(10**8*t+4*x)az # equation of electric field
A = 5 # amplitude of the electric field
omega = 10**8 # angular frequency in radians/sec
f = omega/(2*pi) # frequency in Hz
Beta = 4 # phase constant in rad/m
v_0 = 3*10**8 # speed of light in m/s
lamda = v_0/f # wavelength in m
#results
print "frequency in MHz:",round(f/10**6,3)
print "phase constant in rad/m:",round(Beta,3)
print "wavelength in m:",round(lamda,3)
```

In [10]:

```
from __future__ import division
from math import pi
sigma = 10**-2 # conductivity of earth in mho/m
epsilon_r = 10 # relative permittivity
mu_r = 2 # relative permeability
epsilon_0 = (1/(36*pi))*10**-9 # permittivity in free space
epsilon = epsilon_r*epsilon_0 # permittivity
f1 = 50 # frequency in Hz
omega1 = 2*pi*f1 # angular frequency in rad/sec
print "When frequency = 50Hz:"
k1 = sigma/(omega1*epsilon)
print "K1 is equal to",k1
print "since k1>>1 hence it behaves like a good conductor:"
f2 = 1 # frequency in kHz
f2 = 1*10**3 # frequency in Hz
omega2 = 2*pi*f2 # angular frequency in rad/sec
print "When frequency = 1kHz:"
k2 = sigma/(omega2*epsilon)
print "K2 is equal to",k2
print "since k2>>1 hence it behaves like a good conductor:"
f3 = 1 # frequency in MHz
f3 = 1*10**6 # frequency in Hz
omega3 = 2*pi*f3 # angular frequency in rad/sec
print "When frequency = 1MHz:"
k3 = sigma/(omega3*epsilon)
print "K3 is equal to",k3
print "since k3 = 18 hence it behaves like a moderate conductor:"
f4 = 100 # frequency in MHz
f4 = 100*10**6 # frequency in Hz
omega4 = 2*pi*f4 # angular frequency in rad/sec
print "When frequency = 100MHz:"
k4 = sigma/(omega4*epsilon)
print "K4 is equal to",k4
print "since k4 = 0.18 hence it behaves like a quasi-dielectric:"
f5 = 10 # frequency in GHz
f5 = 10*10**9 # frequency in Hz
omega5 = 2*pi*f5 # angular frequency in rad/sec
print "When frequency = 10GHz:"
k5 = sigma/(omega5*epsilon)
print "K5 is equal to",k5
print "since k5<<1 hence it behaves like a good dielectric:"
```

In [11]:

```
from __future__ import division
from math import sqrt,pi
import cmath
import numpy as np
#variable declaration
f = 60 # frequency in Hz
omega = 2*pi*f # angular frequency in rad/sec
sigma = 5.8*10**7 # conductivity in mho/m
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
epsilon_r = 1 # relative permittivity
mu_r = 1 # relative permeability
#calculations
epsilon = epsilon_r*epsilon_0 # permittivity
mu = mu_0*mu_r # permeability
k = sigma/(omega*epsilon) # ratio
print "ratio k is equal to",k
print "since k>>1 therefore it is very good conductor:"
alpha = sqrt(omega*mu*sigma/2) # attenuation constant in m**-1
Beta = sqrt(omega*mu*sigma/2) # phase constant in m**-1
Gamma = alpha+(1j*Beta) # propagation constant in m**-1
lamda = (2*pi)/Beta # wavelength
eta = cmath.sqrt(((1j*omega*mu)/sigma)) # intrinsic impedence in ohm
v = lamda*f # phase velocity of wave in m/s
#result
print "attenuation constant in m**-1:",round(alpha,2)
print "phase constant in m**-1:",round(Beta,2)
print "propagation constant in m**-1:",np.around(Gamma,2)
print "intrinsic impedence in ohm:",np.around(eta,10)
print "wavelength in cm:",round(lamda*100,2)
print "phase velocity of wave in m/s:",round(v,3)
```

In [12]:

```
from __future__ import division
from math import sqrt,pi
#variable Declaration
f1 = 60 # frequency in Hz
omega1 = 2*pi*f1 # angular frequency in Hz
f2 = 100 # frequency in MHz
f2 = 100*10**6 # frequency in Hz
omega2 = 2*pi*f2 # angular frequency in Hz
sigma = 5.8*10**7 # conductivity in mho/m
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
epsilon_r = 1 # relative permittivity
mu_r = 1 # relative permeability
epsilon = epsilon_r*epsilon_0 # permittivity
mu = mu_0*mu_r # permeability
print "At f = 60Hz"
k1 = (sigma)/(omega1*epsilon) # ratio
print "ratio k is equal to",k1
print "since k>>1 therefore it is very good conductor at f = 60Hz:"
delta1 = (sqrt(2/(omega1*mu*sigma))) # depth of penetration in m
print "depth of penetration delta1 in m:",delta1
print "At f = 100Hz"
k2 = sigma/(omega2*epsilon) # ratio
print "ratio k is equal to",k2
print "since k2>>1 therefore it is very good conductor at f = 100Hz:"
delta2 = (sqrt(2/(omega2*mu*sigma))) # depth of penetration in m
print "depth of penetration delta2 in m:",delta2
```

In [13]:

```
from __future__ import division
from math import sqrt,pi
#variable Declaration
Ic = 10 # conduction current in ampere
epsilon_r = 1 # relative permittivity
epsilon_0 = 8.854*10**-12 # permittivity in free space
epsilon = epsilon_r*epsilon_0 # permittivity
sigma = 5.8*10**7 # conductivity in mho/m
print "when f = 1MHz"
f = 1 # frequency in MHz
f = 1*10**6 # frequency in Hz
Id = (2*pi*f*epsilon*Ic)/sigma # printlacement current
print "displacement current when f = 1MHz in A:",Id
print "when f = 100MHz"
f = 100 # frequency in MHz
f = 100*10**6 # frequency in Hz
Id = (2*pi*f*epsilon*Ic)/sigma # printlacement current
print "displacement current when f = 100MHz in A:",Id
```

In [14]:

```
from __future__ import division
from math import sqrt,pi,sin,cos,radians,log
#variable declaration
Em = 20 # minimum signal level required for vessel under sea water in microV/m
Em = 20*10**-6 # minimum signal level required for vessel under sea water in V/m
E = 100 # electric intensity of wave in V/m
v = 3*10**8 # speed of light in m/s
f = 4 # frequency in MHz
f = 4*10**6 # frequency in Hz
omega = 2*pi*f # angular frequency in Hz
sigma = 4 # conductivity of sea water in mho/m
epsilon_r = 81 # relative permittivity
epsilon_0 = 8.854*10**-12 # permittivity in free space
epsilon = epsilon_r*epsilon_0 # permittivity
mu_r = 1 # relative permeability
mu_0 = 4*pi*10**(-7) # permeability in free space
mu = mu_r*mu_0 # permeability
k = (sigma)/(omega*epsilon) #ratio
print "ratio k is equal to:"
print "ratio:",round(k,3)
print "K is >>1 so sea water is a good conductor"
eta_1 = 377 # intrinsic impedance in free space in ohm
alpha_1 = 0 # attenuation constant in free space in m**-1
#calculations
beta_1 = omega/v # phase constant in m**-1
mageta_2 = sqrt((omega*mu)/sigma) # magnitude of eta_2(intrinsic impedance of sea water in ohm)
argeta_2 = 45 # argument of eta_2 in degrees
eta_2 = mageta_2*cos(radians(argeta_2))+(1j*mageta_2*sin(radians(argeta_2))) #intrinsic impedance in complex form (r*cos(theta)+1j*r*sin(theta))
TC = 2*eta_2/(eta_1+eta_2) # transmission cofficient
Et = abs(TC)*E # transmitted electric field in V/m
alpha_2 = sqrt((omega*mu*sigma)/2) # attenuation constant for sea water in m**-1
# formula: Et*exp(-alpha_2*d) = Em
d = -(1/alpha_2)*(log(Em/Et)) # depth in the sea that can be reached by the aeroplane in m
#result
print "depth in the sea that can be reached by the aeroplane in m:",round(d,5)
# note 1: the value of alpha_2 in book is 7.905 but it is "7.94" exactly calculated by python.
#note 2 : The correct answer of the Depth(d) is "1.41095" the answer in the book is wrong.
```

In [15]:

```
from __future__ import division
from math import sqrt
#variable declaration
eta_0=377 # intrinsic impedance in free space in ohm
print "E=sin(omega*t-beta*z)ax+2*sin(omega*t-beta*z+75)ay # electric field in V/m"
Ex=1 # magnitude of Ex
Ey=2 # magnitude of Ey
#calculations
E=sqrt(Ex**2+Ey**2) # resultant magnitude
Pav=((1/2)*E**2)/(eta_0) # power per unit area conveyed by the wave in free space
#results
print "power per unit area conveyed by the wave in free space in mW/m**2:",round(Pav*1000,3)
```

In [16]:

```
from __future__ import division
from math import sqrt,pi
#variable declaration
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
epsilon_r = 4 # relative permittivity
mu_r = 1 # relative permeability
epsilon = epsilon_r*epsilon_0 # permittivity
mu = mu_0*mu_r # permeability
H = 5 # magnitude of magnetic field in mA/m
H = 5*10**-3 # magnitude of magnetic field in A/m
#calculations
eta = sqrt(mu/epsilon) # intrinsic impedence in ohm
E = H*sqrt(mu/epsilon) # magnitude of electric field
P_av = E**2/(2*eta) # average power
W_E = epsilon*E**2 # maximum energy density of the wave
#results
print "Average power in micro*w/m**2:",round(P_av*10**6,2)
print "maximum energy density of the wave in PJ/m*3:",round(W_E*10**12,3)
#note: P_av is = 2353.75 in book but it is 2354.58 correctly calculated by python.
```

In [17]:

```
from __future__ import division
from math import sqrt,pi
#variable declaration
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
epsilon_r = 1 # relative permittivity
mu_r = 1 # relative permeability
epsilon = epsilon_r*epsilon_0 # permittivity
mu = mu_0*mu_r # permeability
E = 100*sqrt(pi) # magnitude of electric field in V/m
#calculations
W_E = (1/2)*epsilon*E**2 # electric energy density of the wave
W_H = W_E # as the energy density is equal to that of magnetic field for a pla`ne travelling wave
W_T = W_E+W_H # total energy density
#results
print "electric energy density of the wave in nJ/m**3:",round(W_E*10**9,3)
print "magnetic energy density of wave in nJ/m**3:",round(W_H*10**9,3)
print "Total energy density in nJ/m**3:",round(W_T*10**9,3)
```

In [18]:

```
from __future__ import division
from math import sqrt,pi
#variable Declaration
sigma = 5 # conductivity of sea water in mho/m
f1 = 25 # frequency in kHz
f1 = 25*10**3 # frequency in Hz
omega1 = 2*pi*f1 # angular frequency in Hz
f2 = 25 # frequency in MHz
f2 = 25*10**6 # frequency in Hz
omega2 = 2*pi*f2 # angular frequency in Hz
epsilon_r = 81 # relative permittivity
epsilon_0 = 8.854*10**(-12) # permittivity in free space
epsilon = epsilon_r*epsilon_0 # permittivity
mu_r = 1 # relative permeability
mu_0 = 4*pi*10**(-7) # permeability in free space
mu = mu_r*mu_0 # permeability
#calculations and results
print "when frequency = 25kHz"
alpha_1 = omega1*sqrt((mu*epsilon)/2*(sqrt(1+(sigma**2/(omega1**2*epsilon**2)))-1)) # attenuation constant when f = 25kHz
# formula: exp(-alpha*x) = 0.1
x1 = 2.3/alpha_1 # transmitted distance in m
print "transmitted distance in m:",round(x1,3)
print "when frequency = 25MHz"
alpha_2 = omega2*sqrt((mu*epsilon)/2*(sqrt(1+(sigma**2/(omega2**2*epsilon**2)))-1)) # attenuation constant when f = 25MHz
x2 = 2.3/alpha_2 # transmitted distance in m
print "transmitted distance in m:",round(x2,3)
# note: the values of epsilon_r = 81 and of mu_r = 1 for sea water which are not given in the book.
```

In [19]:

```
from __future__ import division
from math import sqrt,pi,radians,asin,cos,sin,degrees
#variable Declaration
E_i = 1 # magnitude of incident electric field in mV/m
E_i = 1*10**-3 # magnitude of incident electric field in V/m
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
theta_i = 15 # incident angle in degrees
epsilon_r1 = 8.5 # relative permittivity of medium 1
mu_r1 = 1 # relative permeability of medium 1
epsilon1 = epsilon_r1*epsilon_0 # permittivity
mu1 = mu_0*mu_r1 # permeability
eta1 = sqrt(mu1/epsilon1) # intrinsic impedence of medium 1 in ohm
epsilon2 = epsilon_0 # permittivity of medium 2
mu2 = mu_0 # permeability of medium 2
eta2 = sqrt(mu2/epsilon2) # intrinsic impedence of medium 2 in ohm
#calculations and result
# formula : sin(theta_i)/sin(theta_t) = sqrt(epsilon2/epsilon1)
theta_t = asin(sin(radians(theta_i)))/(sqrt(epsilon2/epsilon1)) # transmitted angle in degrees
E_r = (E_i*(((eta2*cos(radians(theta_i))))-(eta1*cos(radians((theta_i))))))/((eta2*cos(radians(theta_i)))+(eta1*cos(radians(theta_i)))) # reflection cofficient of electric field
print "reflection cofficient of electric field in mV/m:",round(E_r*1000,3)
H_i = E_i/eta1 # incident cofficient of magnetic field
print "incident cofficient of magnetic field in micro*A/m:",round(H_i*10**6,3)
H_r = E_r/eta1 # reflection cofficient of electric field
print "reflection cofficient of magnetic field in micro*A/m:",round(H_r*10**6,3)
#note : minute difference in decimel in the value of H_i and H_r.
```

In [1]:

```
from __future__ import division
from math import pi,sqrt
#variable declaration
sigma = 5.8*10**7 # conductivity in mho/m
f = 2 # frequency in MHz
f = 2*10**6 # frequency in Hz
omega = 2*pi*f # angular frequency in rad/sec
E = 2 # magnitude of electric field in mV/m
E = 2*10**-3 # magnitude of electric field in V/m
epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m
mu_0 = 4*pi*10**-7 # permeability in free space in H/m
epsilon_r = 1 # relative permittivity
mu_r = 1 # relative permeability
epsilon = epsilon_r*epsilon_0 # permittivity
mu = mu_0*mu_r # permeability
# calculations
eta = sqrt(mu*omega/sigma) # intrinsic impedence in ohm
P_av = (1/2)*E**2/eta # average power density anbsorbed by copper
#result
print "average power density absorbed by copper in mW/m**2:",round(P_av*1000,2)
```