# Chapter 11: Electromagnetic Theory¶

## Example 11.1, Page 559¶

In :
from math import *

#Variable declaration
H_0 = 1;   # Amplitude off field vector,in A/m
mu_0 = 12.56e-7;   # Permeability,in weber/A-m
eps = 8.85e-12;   # Permittivity in free space,in C/N-meter-square

#Calculations
# From the relation between the amplitude of the field vector E and vector H of an EM wave in free space
E_0 = H_0*(sqrt(mu_0/eps));

#Result
print "The amplitude of field vector E in free space = %5.1f V/m"%E_0

The amplitude of field vector E in free space = 376.7 V/m


## Example 11.2, Page 560¶

In :
#Variable declaration
E_o = 1e+3;   # Amplitude field vector in free space,N/C
c = 3e+8;   # Speed of light,in m/s

#Calculations
# From the relation between the amplitude of the field vector E and vector H of an EM wave in free space E_o = H_o*(sqrt(mu_o/eps))and B_o = mu_o*H_o, we have
B_o = E_o/c;

#Result
print "The maximum value of magnetic induction vector = %4.2e weber/A-m"%B_o

The maximum value of magnetic induction vector = 3.33e-06 weber/A-m


## Example 11.3, Page 560¶

In :
#Variable declaration
sigma = 5;   # Conductivity of the conducting medium, mho/m
eps_r = 8.85e-12;   # Relative electrical permittivity of medium, F/m
eps_0 = 1;    # Electrical permittivity of free space, F/m
E0 = 250;   # Amplitude of applied electric field, V/m

#Calculations
J = sigma*E0;    # Amplitude of conduction current density, A/metre-square
J_D = eps_r*eps_0*E0*1e+010;   # Amplitude of displacement current density, A/metre-square
omega = sigma/(eps_0*eps_r);    # Frequency at which J = J_D

#Results
print "The conduction current density = %3dsin(10^10t) A/metre-quare"%J
print "The displacement current density = %5.3fcos(10^10t) A/metre-quare"%J_D   #incorrect answer in the textbook
print "The frequency at which J = J_D is %3.1e Hz"%omega

The conduction current density = 1250sin(10^10t) A/metre-quare
The displacement current density = 22.125cos(10^10t) A/metre-quare
The frequency at which J = J_D is 5.6e+11 Hz


## Example 11.8, Page 565¶

In :
from math import *

#Variable declaration
P = 1000;   # Energy radiated by the lamp, watt
r = 2;   # Distance from the source at which the electric field intensity is given, m

#Calculations
S = P/(4*pi*r**2);      # Magnitude of Poynting vector, W/metre-square
# As wave imepdence, Z0 = E/H = 377 and H = E/377, so that with E*H = S we have
E = 377
E = sqrt(S*E)

#Result
print "The average value of the intensity of electric field of radiation = %4.1f V/m"%(E)

The average value of the intensity of electric field of radiation = 86.6 V/m


## Example 11.9, Page 566¶

In :
from math import *

#Variable declaration
S = 2*4.186/60*1e+04;   # Solar constant, J/s/metre-square
# From the poynting vector S = E*H
C = 377;   # Wave Impedence, ohm

#Calculations
E = sqrt(S*C);      # Electric field of radiation, V/m
H = E/C;            # Magnetic field of radiation, A/m
E0 = E*sqrt(2);     # Amplitude of electric field of radiation, V/m
H0 = H*sqrt(2);     # Amplitude of magnetic field of radiation, A/m

#Results
print "The amplitude of electric field of radiation = %6.1f V/m"%E0    #incorrect answer in the textbook
print "The amplitude of magnetic field of radiation = %5.3f V/m"%H0

The amplitude of electric field of radiation = 1025.7 V/m
The amplitude of magnetic field of radiation = 2.721 V/m


## Example 11.12, Page 569¶

In :
from math import *

#Variable declaration
sigma = 3.54e+007;   # Electrical conductivity of Al, mho per metre
mu = 12.56e-007;   # Permeability of the medium, weber/A-m
f = 71.6e+06;    # Frequency of the wave, Hz

#Calculations
omega = 2*pi*f;   # Angular frequency of the wave, rad per sec
delta = sqrt(2/(sigma*mu*omega));    # Skin depth of the EM wave in Al, m

#Result
print "The skin depth of an EM-wave in Al = %2.0f micron"%(delta/1e-06)

The skin depth of an EM-wave in Al = 10 micron


## Example 11.14, Page 571¶

In :
from math import *

#Variable declaration
sigma = 5.;   # Electrical conductivity, mho per metre
mu = 12.56e-007;   # Permeability of the medium, weber/A-m
eps_0 = 8.85e-012;   # Electric permittivity of free space, C-square/N-m-square

#Calculations&Results
eps = 70*eps_0;    # Electric permittivity of the medium, C-square/N-m-square
delta = 2/sigma*sqrt(eps/mu); # The skin depth and attenuation constant of sea water
print "The skin depth of an EM-wave in sea water = %6.4f m"%delta
Beta = 1/delta;    # The attenuation constant of sea water, per metre
print "The attenuation constant of the sea water = %6.2f m"%Beta

The skin depth of an EM-wave in sea water = 0.0089 m
The attenuation constant of the sea water = 112.57 m