# chapter7 :Maxwell's Equations and Electromagnetic Waves¶

## example 7.1;page no:304¶

In :
#cal of Average value of electric field
#intiation of all variables
#Given that
import math
p = 1000 # power in watt
d = 2 # Distance from lamp in m
epsilon_0 = 8.854e-12 # Permittivity of free space
mu_0 = 4*math.pi*1e-7 # Permeability of free space
print("Example 7.1,page no:304")
s = p/(4*math.pi*d**2)# Calculation of pointing vector
E_H_ratio = math.sqrt(mu_0/epsilon_0) # Calculation of ratio of Electric field and magnetic field
E= math.sqrt(E_H_ratio*s) # Calculation of  Electric field
print("Average value of electric field at distance m in Volt/m:"),round(E,2)
# Answer in book is 48.87 volt/m which is due to wrong calculation at intermediate steps

Example 7.1,page no:304
Average value of electric field at distance m in Volt/m: 86.57


## example 7.2;page no:304¶

In :
#cal of Average value of electric field and magnetic field
#intiation of all variables
#Given that
import math
p = 2 # power in cal/min/cm^2
epsilon_0 = 8.854e-12 # Permittivity of free space
mu_0 = 4*math.pi*1e-7 # permeability of free space
print("Example 7.2,page no:304")
s = p*4.2e4/60 # Calculation of pointing vector
E_H_ratio = math.sqrt(mu_0/epsilon_0) # Calculation of ratio of Electric field and magnetic field
E= math.sqrt(E_H_ratio*s) # Calculation of Electric field
H = s/E # Calculation of Electric field
print("Average value of electric field  in Volt/m:"),round(E*math.sqrt(2),1)
print("Average value of magnetic field in Amp turn/m:"),round(H*math.sqrt(2),3)

Example 7.2,page no:304
Average value of electric field  in Volt/m: 1027.1
Average value of magnetic field in Amp turn/m: 2.726


## example 7.3;page no:305¶

In :
#cal of Skin depth penetration
#intiation of all variables
#Given that
import math
mu_0 = 4*math.pi*1e-7 # permeability of free space
mu = mu_0 #permeability of silver
sigma = 3e7 # conductivity in mhos/m
f = 1e8 # frequency in Hz
print("Example 7.3,page no:305")
omega = 2*math.pi/f # Calculation of time period
delta = math.sqrt(2/(omega*sigma*mu)) # Calculation of skin depth penetration
Delta = (delta/100)*100 # Rounding off
print("Skin depth penetration in cm:"),round(Delta*1e-6,4)

Example 7.3,page no:305
Skin depth penetration in cm: 0.0009


## example 7.5;page no:307¶

In :
#cal of Frequency required for penetration of depth and sea water can be considered as good conductor
#intiation of all variables
#Given that
import math
k = 80 # relative Dielectric constant of sea water
epsilon_0 = 1/9e9 # Permittivity of free space
epsilon = 80*epsilon_0 # Permittivity of free space
sigma = 4.3 # conductivity in mho/m
delta = 10 # penetration depth in cm
mu_0 = 4*math.pi*1e-7 # permeability f free space
F = 1e8 # Given frequency in Hz
print("Example 7.5,page no:307")
f = (1/(math.pi*mu_0*sigma))/(delta*1e-2)**2 # Calculation of frequency
print("Frequency required for penetration of depth in MHz="),round(f/10**6)
omega = 2*math.pi*F
x = 2*sigma/(epsilon*omega)
if x>1:
print("Sea water is good conductor at frequency lesser than 1e8 Hz")

Example 7.5,page no:307
Frequency required for penetration of depth in MHz= 6.0
Sea water is good conductor at frequency lesser than 1e8 Hz


## example 7.7;page no:308¶

In :
#cal of Penetration depth and frequency
#intiation of all variables
#Given that
import math
k = 12 # relative Dielectric constant of sea water
epsilon_0 = 1/9e9 # Permittivity of free space
sigma = 2 # conductivity in mho/cm
mu_0 = 4*math.pi*1e-7 # permeability f free space
f= 1e9 # Given frequency in Hz
F = 1e6 # Given frequency in Hz
print("Example 7.7,page no:308")
delta = math.sqrt(2/(2*math.pi*F*mu_0*sigma*100)) # Calculation of frequency
print("For MHz frequency, Penetration depth in cm:"),round(F/10**6,1),round(delta*100,1)
omega = 2*math.pi*f
x = 2*sigma*100/(k*epsilon_0*omega)
if x>1:
print("Silicon is good conductor at frequency lesser than 1e9 Hz:")
# Answer in book is 3.6 cm

Example 7.7,page no:308
For MHz frequency, Penetration depth in cm: 1.0 3.6
Silicon is good conductor at frequency lesser than 1e9 Hz:


## example 7.8;page no:309¶

In :
#cal of frequency of incident electromagnetic wave
#intiation of all variables
#Given that
import math
mu_0 = 4*math.pi*1e-7 # permeability of free space
mu = mu_0 #permeability of silver
sigma = 5.8e7 # conductivity in simens /m
delta = 0.1 # Skin depth penetration in mm
print("Example 7.8,page no:309")
f = 2/((delta*1e-3)**2*sigma*mu*2*math.pi) # Calculation of skin depth penetration
print("Required frequency in Hz:"),round(f,1)
print("The incident electromagnetic wave is the radio part of spectrum.")
# Answer in book is 3.36e5 Hz. Difference is due to approximation at intermediate stages

Example 7.8,page no:309
Required frequency in Hz: 436729.2
The incident electromagnetic wave is the radio part of spectrum.


## example 7.9;page no:310¶

In :
 #cal of Skin depth penetration
#intiation of all variables
#Given that
import math
mu_0 = 4*math.pi*1e-7 # Permeability of free space
mu = mu_0 #Permeability of silver
sigma = 3e7 # conductivity in mhos/m
f = 1e10 # frequency in Hz
print("Example 7.9,page no:310")
delta = math.sqrt(1/(math.pi*sigma*f*mu)) # Calculation of skin depth penetration
print("Skin depth penetration in micrometre:"),round(delta*1e6,2)
# Answer in book is 0.93 micrometer

Example 7.9,page no:310
Skin depth penetration in micrometre: 0.92


# example 7.10;page no:310¶

In :
#cal of Average value of electric field and magnetic field
#intiation of all variables
#Given that
import math
p = 500. # power in watt
d = 1. # Distance from lamp in m
epsilon_0 = 8.854e-12 # Permittivity of free space
mu_0 = 4*math.pi*1e-7 # Permeability of free space
print("Example 7.10,page no:310")
s = p/(4.*math.pi*d**2)# Calculation of pointing vector
E_H_ratio = math.sqrt(mu_0/epsilon_0) # Calculation of ratio of Electric field and magnetic field
H = s/E_H_ratio # Calculation of Electric field
h = (H*100.)/100. # rounding off for 2 decimal places
E= p/(4.*math.pi*h) # Calculation of Electric field
print("Average value of electric field at distance  m in Volt/m:"),round(E,1)
print("Average value of magnetic field at distance  m in Amp-turn/m:"),round(h,3)

Example 7.10,page no:310
Average value of electric field at distance  m in Volt/m: 376.7
Average value of magnetic field at distance  m in Amp-turn/m: 0.106


## example 7.11;page no:312¶

In :
#cal of frequency of incident radiation and location in electromagnetic
#intiation of all variables
#Given that
import math
mu_0 = 4*math.pi*1e-7 # Permeability of free space
mu = mu_0 #Permeability of silver
sigma = 3.5e7 # conductivity in simens /m
delta = 0.03 # Skin depth penetration in mm
print("Example 7.11,page no:312")
f = 2/((delta*1e-3)**2*sigma*mu*2*math.pi) # Calculation of skin depth penetration
print("Required frequency in MHz:"),round(f/1e6,0)
print("The incident electromagnetic wave is the radio part of spectrum")

Example 7.11,page no:312
Required frequency in MHz: 8.0
The incident electromagnetic wave is the radio part of spectrum


## example 7.12;page no:312¶

In :
#cal of Solar energy received during solar eclipse
#intiation of all variables
#Given that
import math
p = 3.8e26 # power radiated by moon in watt
d_sun = 1.44e11 # Distance between sun and earth in meter
d_moon = 3e8 #Distance between moon and earth in meter
epsilon_0 = 8.854e-12 # Permittivity of free space
mu_0 = 4*math.pi*1e-7 # Permeability of free space
print("Example 7.12,page no:312")
s = p/(4*math.pi*d_sun**2)# Calculation of solar energy received during solar eclipse in watt /m^2
S = s*60/(4.2*1e4) # Unit conversion
print("Solar energy received during solar eclipse in Cal per min per m^2:"),round(S,1)
# Ansewr in book is 2.1 cal per min per m^2

Example 7.12,page no:312
Solar energy received during solar eclipse in Cal per min per m^2: 2.1


## example 7.13;page no:313¶

In :
#cal of Skin depth penetration
#intiation of all variables
#Given that
import math
mu_0 = 4*math.pi*1e-7 # Permeability of free space
mu = mu_0 #Permeability of silver
sigma = 3.5e7 # conductivity in simens /m
lamda = 6328 # Wavelength in angstrom
c = 3e8# Speed of light in m/sec
print("Example 7.13,page no:313")
f = c/(lamda*1e-10)
omega = 2*math.pi/f # Calculation of time period
f = c/(lamda*1e-10) # Calculation of frequency in Hz
delta = math.sqrt(1/(math.pi*f*sigma*mu)) # Calculation of skin depth penetration
print("Skin depth penetration in nm:"),round(delta*1e9,1)
# Answer in book is 3.9 mm, unit used in book is wrong

Example 7.13,page no:313
Skin depth penetration in nm: 3.9