{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 2 : Maxwell's Equations and Electromagnetic Waves"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.8,Page Number 112"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"magnetic field in region 2 in A/m: [ 2.4 1.5 -3. ]\n",
"magnitude of magnetic field in region 2 in A/m: 4.124\n"
]
}
],
"source": [
"from __future__ import division\n",
"import numpy as np\n",
"from math import pi\n",
"\n",
"#variable delaration\n",
"mu_0 = 4*pi*10**(-7) # permeability in free space\n",
"mu_r1 = 3 # region 1 relative permeability\n",
"mu_r2 = 5 # region 2 relative permeability\n",
"mu_1 = mu_r1*mu_0 # region 1 permeability\n",
"mu_2 = mu_r2*mu_0 # region 2 permeability\n",
"\n",
"#calculations\n",
"H1 = np.array([4,1.5,-3]) # magnetic field in region 1 in A/m\n",
"Ht1 = np.array([0,1.5,-3]) # tangential component of magnetic field H1\n",
"Hn1 = np.array([4,0,0]) # normal component of magnetic field H1\n",
"Ht2 = np.array([0,1.5,-3]) # as tangential componenet of magnetic field H2 = tangential component of magnetic field H1\n",
"Hn2 = (mu_1/mu_2)*Hn1 # normal component of magnetic field H2\n",
"H2 = Ht2+Hn2 # magnetic field in region 2 in A/m\n",
"h2 = np.linalg.norm(H2) # magnitude of the magnetic field H2 in A/m\n",
"\n",
"#results\n",
"print \"magnetic field in region 2 in A/m:\",np.around(H2,2)\n",
"print \"magnitude of magnetic field in region 2 in A/m:\",round(h2,3) \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.9,Page Number 113"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"electric field in region 2 in V/m: [ 0.5 2. 3. ]\n",
"electric flux density in region 2 in C/m**2: [ 8.85400000e-12 3.54160000e-11 5.31240000e-11]\n"
]
}
],
"source": [
"from __future__ import division\n",
"import numpy as np\n",
"\n",
"#variable Declaration\n",
"epsilon_0 = 8.854*10**(-12) # permittivity in free space\n",
"sigma_1 = 0 #conductivity of medium 1\n",
"sigma_2 = 0 #conductivity of medium 2\n",
"epsilon_r1 = 1 # region 1 relative permittivity\n",
"epsilon_r2 = 2 # region 2 relative permittivity\n",
"\n",
"#calculations\n",
"epsilon_1 = epsilon_r1*epsilon_0 # region 1 permittivity\n",
"epsilon_2 = epsilon_r2*epsilon_0 # region 2 permittivity\n",
"E1 = np.array([1,2,3]) # Electric field in region 1 in V/m\n",
"Et1 = np.array([0,2,3]) # tangential component of electric field E1\n",
"En1 = np.array([1,0,0]) # normal component of electric field E1\n",
"Et2 = np.array([0,2,3]) # as tangential componenet of electric field E2 = tangential component of electric field E1\n",
"En2 = (epsilon_1/epsilon_2)*En1 # normal component of electric field E2\n",
"E2 = Et2+En2 # electric field in region 2 in V/m\n",
"Dt1 = epsilon_0*Et1 # tangential component of electric flux density D1\n",
"D2 = epsilon_2*E2 # electric flux density in region 2 in C/m**2\n",
"\n",
"\n",
"#Results\n",
"print \"electric field in region 2 in V/m:\",np.around(E2,2)\n",
"print \"electric flux density in region 2 in C/m**2:\",D2 \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.12,Page Number 116"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"eta_0 = E/H = 377*cos(10**8*t-Beta*z)/cos(10**8*t-Beta*z) = > E/H = 377\n",
"intrinsic impedence in ohm: 377\n",
"frequency in MHz: 15.915\n",
"phase constant in rad/m: 0.333\n",
"wavelength in m: 18.85\n"
]
}
],
"source": [
"from __future__ import division\n",
"import numpy as np\n",
"from math import pi\n",
"\n",
"#variable Declaration\n",
"\n",
"# H = cos(10**8*t-Beta*z)ay # magnetic field in A/m\n",
"# E = 377*cos(10**8*t-Beta*z)ax # electric field in V/m\n",
"omega = 10**8 # angular frequency in Hz\n",
"v_0 = 3*10**8 # speed of light in m/s\n",
"\n",
"\n",
"#calculations\n",
"f = omega/(2*pi) # frequency in Hz\n",
"lamda = v_0/f # wavelength in m\n",
"Beta = (2*pi)/lamda # phase constant in rad/m\n",
"print \"eta_0 = E/H = 377*cos(10**8*t-Beta*z)/cos(10**8*t-Beta*z) = > E/H = 377\"\n",
"eta_0 = abs(377) # intrinsic impedence in ohm\n",
"\n",
"\n",
"\n",
"#Results\n",
"print \"intrinsic impedence in ohm:\",eta_0\n",
"print \"frequency in MHz:\",round(f/(10**6),3)\n",
"print \"phase constant in rad/m:\",round(Beta,3)\n",
"print \"wavelength in m:\",round(lamda,3)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.14,Page Number 116"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"propagation constant in m**-1: 2.094j\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"import numpy as np\n",
"\n",
"#Variable Declaration\n",
"f = 100 # frequency in MHz\n",
"f = 100*10**6 # frequency in Hz\n",
"v_0=3*10**8 # speed of light in m/s\n",
"\n",
"\n",
"# formula : Gamma = omega(j)*sqrt(mu_0*epsilon_0)=omega(j)/v_0 =(2j*pi*f)/v_0\n",
"Gamma =(2j*pi*f)/(v_0) # propagation constant\n",
"\n",
"\n",
"#result\n",
"print \"propagation constant in m**-1:\",np.around(Gamma,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.15,Page Number 116"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"amplitude of the magnetic field in A/m: 48\n",
"frequency in MHz: 15.915\n",
"phase constant in rad/m: 40.0\n",
"wavelength in m: 0.157\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"#Variable Declaration\n",
"\n",
"# H(z,t) = 48*cos(10**8*t+40*z)ay # equation of magnetic field \n",
"A = 48 # amplitude of the magnetic field in A/m\n",
"omega = 10**8 # angular frequency in radians/sec\n",
"Beta = 40 # phase constant in rad/m\n",
"\n",
"#Calculations\n",
"f = omega/(2*pi) # frequency in Hz\n",
"lamda = (2*pi)/Beta # wavelength in m\n",
"\n",
"\n",
"#results\n",
"print \"amplitude of the magnetic field in A/m:\",A\n",
"print \"frequency in MHz:\",round(f/10**6,3)\n",
"print \"phase constant in rad/m:\",round(Beta,3)\n",
"print \"wavelength in m:\",round(lamda,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.16,Page Number 117"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"magnitude of electric field in V/m in free space: 753.982\n",
"magnitude of electric field in V/m: 376.734\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"\n",
"#Variable Declaration\n",
"\n",
"H = 2 # ampliutude of magnetic field in A/m\n",
"sigma = 0 # conductivity\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"\n",
"#calculations\n",
"mu = mu_0 # permeability in F/m\n",
"epsilon = 4*epsilon_0 # permittivity in F/m\n",
"Eta_0 = 120*pi # intrinsic impedence in free space in ohm\n",
"E_free = Eta_0*H # electric field in V/m\n",
"\n",
"\n",
"#results\n",
"print \"magnitude of electric field in V/m in free space:\",round(E_free,3)\n",
"Eta = sqrt(mu/epsilon) # intrinsic impedence in ohm\n",
"E = Eta*H # magnitude of electric field\n",
"print \"magnitude of electric field in V/m:\",round(E,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.17,Page Number 117"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"propagation constant im m**-1: 18.862j\n",
"intrinsic impedence in ohm: 125.578\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"import numpy as np\n",
"\n",
"\n",
"#variable Declaration\n",
"\n",
"sigma = 0 # conductivity in mho/m\n",
"f = 0.3 # frequency in GHz\n",
"f = 0.3*10**9 # frequency in Hz\n",
"omega = 2*pi*f # angular frequency in rad/sec\n",
" # formula : Gamma = sqrt(1j*omega*mu*(sigma+1j*omega*epsilon)) = 1j*omega*sqrt(mu*epsilon)\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"epsilon = 9*epsilon_0 # permittivity in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"mu = mu_0 # permeability in H/m\n",
"Gamma = 1j*omega*sqrt(mu*epsilon) # propagation constant im m**-1\n",
"\n",
"\n",
"#results\n",
"\n",
"print \"propagation constant im m**-1:\",np.around(Gamma,3)\n",
" # formula : eta = sqrt((1j*omega*mu)/(sigma+omega*epsilon)) = sqrt(mu/epsilon)\n",
"eta = sqrt(mu_0/(9*epsilon_0)) # intrinsic impedence in ohm\n",
"print \"intrinsic impedence in ohm:\",round(eta,3)\n",
"\n",
"\n",
"\n",
"# note : answer in the book is wrong.\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.18,Page Number 118"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"frequecy in MHz: 600.0\n",
"relative permittivity: 4.0\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"#variable declaration\n",
"\n",
"lamda = 0.25 # wavelength in m\n",
"v = 1.5*10**10 # velocity of propagation of wave in cm/sec\n",
"v = 1.5*10**8 # velocity of propagation of wave in m/sec\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"mu = mu_0 # permeability in H/m\n",
"v_0 = 3*10**8 # speed of light in m/s\n",
"f = v/lamda # frequency in Hz\n",
" # formula : v = 1/(mu*epsilon) = 1/(mu_0*epsilon_0*epsilon_r) = v_0/sqrt(epsilon_r)\n",
"epsilon_r = (v_0/v)**2 # relative permittivity\n",
"\n",
"\n",
"#results\n",
"print \"frequecy in MHz:\",round(f/10**6,3)\n",
"print \"relative permittivity:\",epsilon_r\n",
"\n",
"\n",
" # note : answer in the book is wrong.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.19,Page Number 118"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"frequency in MHz: 15.915\n",
"phase constant in rad/m: 4.0\n",
"wavelength in m: 18.85\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"#variable declaration and calculations\n",
"\n",
"#E = 5*sin(10**8*t+4*x)az # equation of electric field \n",
"\n",
"A = 5 # amplitude of the electric field\n",
"omega = 10**8 # angular frequency in radians/sec\n",
"f = omega/(2*pi) # frequency in Hz\n",
"Beta = 4 # phase constant in rad/m\n",
"v_0 = 3*10**8 # speed of light in m/s\n",
"lamda = v_0/f # wavelength in m\n",
"\n",
"\n",
"#results\n",
"print \"frequency in MHz:\",round(f/10**6,3)\n",
"print \"phase constant in rad/m:\",round(Beta,3)\n",
"print \"wavelength in m:\",round(lamda,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.20,Page Number 119"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"When frequency = 50Hz:\n",
"K1 is equal to 360000.0\n",
"since k1>>1 hence it behaves like a good conductor:\n",
"When frequency = 1kHz:\n",
"K2 is equal to 18000.0\n",
"since k2>>1 hence it behaves like a good conductor:\n",
"When frequency = 1MHz:\n",
"K3 is equal to 18.0\n",
"since k3 = 18 hence it behaves like a moderate conductor:\n",
"When frequency = 100MHz:\n",
"K4 is equal to 0.18\n",
"since k4 = 0.18 hence it behaves like a quasi-dielectric:\n",
"When frequency = 10GHz:\n",
"K5 is equal to 0.0018\n",
"since k5<<1 hence it behaves like a good dielectric:\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi\n",
"\n",
"sigma = 10**-2 # conductivity of earth in mho/m\n",
"epsilon_r = 10 # relative permittivity\n",
"mu_r = 2 # relative permeability\n",
"epsilon_0 = (1/(36*pi))*10**-9 # permittivity in free space\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"f1 = 50 # frequency in Hz\n",
"omega1 = 2*pi*f1 # angular frequency in rad/sec\n",
"print \"When frequency = 50Hz:\"\n",
"k1 = sigma/(omega1*epsilon)\n",
"print \"K1 is equal to\",k1\n",
"print \"since k1>>1 hence it behaves like a good conductor:\"\n",
"f2 = 1 # frequency in kHz\n",
"f2 = 1*10**3 # frequency in Hz\n",
"omega2 = 2*pi*f2 # angular frequency in rad/sec\n",
"print \"When frequency = 1kHz:\"\n",
"k2 = sigma/(omega2*epsilon)\n",
"print \"K2 is equal to\",k2\n",
"print \"since k2>>1 hence it behaves like a good conductor:\"\n",
"f3 = 1 # frequency in MHz\n",
"f3 = 1*10**6 # frequency in Hz\n",
"omega3 = 2*pi*f3 # angular frequency in rad/sec\n",
"print \"When frequency = 1MHz:\"\n",
"k3 = sigma/(omega3*epsilon)\n",
"print \"K3 is equal to\",k3\n",
"print \"since k3 = 18 hence it behaves like a moderate conductor:\"\n",
"f4 = 100 # frequency in MHz\n",
"f4 = 100*10**6 # frequency in Hz\n",
"omega4 = 2*pi*f4 # angular frequency in rad/sec\n",
"print \"When frequency = 100MHz:\"\n",
"k4 = sigma/(omega4*epsilon)\n",
"print \"K4 is equal to\",k4\n",
"print \"since k4 = 0.18 hence it behaves like a quasi-dielectric:\"\n",
"f5 = 10 # frequency in GHz\n",
"f5 = 10*10**9 # frequency in Hz\n",
"omega5 = 2*pi*f5 # angular frequency in rad/sec\n",
"print \"When frequency = 10GHz:\"\n",
"k5 = sigma/(omega5*epsilon)\n",
"print \"K5 is equal to\",k5\n",
"print \"since k5<<1 hence it behaves like a good dielectric:\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.21,Page Number 120"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ratio k is equal to 1.73763020468e+16\n",
"since k>>1 therefore it is very good conductor:\n",
"attenuation constant in m**-1: 117.21\n",
"phase constant in m**-1: 117.21\n",
"propagation constant in m**-1: (117.21+117.21j)\n",
"intrinsic impedence in ohm: (2.0209e-06+2.0209e-06j)\n",
"wavelength in cm: 5.36\n",
"phase velocity of wave in m/s: 3.216\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"import cmath\n",
"import numpy as np\n",
"\n",
"#variable declaration\n",
"f = 60 # frequency in Hz\n",
"omega = 2*pi*f # angular frequency in rad/sec\n",
"sigma = 5.8*10**7 # conductivity in mho/m\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"epsilon_r = 1 # relative permittivity\n",
"mu_r = 1 # relative permeability\n",
"\n",
"\n",
"#calculations\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu = mu_0*mu_r # permeability\n",
"k = sigma/(omega*epsilon) # ratio\n",
"print \"ratio k is equal to\",k\n",
"print \"since k>>1 therefore it is very good conductor:\"\n",
"alpha = sqrt(omega*mu*sigma/2) # attenuation constant in m**-1\n",
"Beta = sqrt(omega*mu*sigma/2) # phase constant in m**-1\n",
"Gamma = alpha+(1j*Beta) # propagation constant in m**-1\n",
"lamda = (2*pi)/Beta # wavelength\n",
"eta = cmath.sqrt(((1j*omega*mu)/sigma)) # intrinsic impedence in ohm\n",
"v = lamda*f # phase velocity of wave in m/s\n",
"\n",
"\n",
"#result\n",
"print \"attenuation constant in m**-1:\",round(alpha,2)\n",
"print \"phase constant in m**-1:\",round(Beta,2)\n",
"print \"propagation constant in m**-1:\",np.around(Gamma,2)\n",
"print \"intrinsic impedence in ohm:\",np.around(eta,10)\n",
"print \"wavelength in cm:\",round(lamda*100,2)\n",
"print \"phase velocity of wave in m/s:\",round(v,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.22,Page Number 120"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"At f = 60Hz\n",
"ratio k is equal to 1.73763020468e+16\n",
"since k>>1 therefore it is very good conductor at f = 60Hz:\n",
"depth of penetration delta1 in m: 0.00853160047351\n",
"At f = 100Hz\n",
"ratio k is equal to 10425781228.1\n",
"since k2>>1 therefore it is very good conductor at f = 100Hz:\n",
"depth of penetration delta2 in m: 6.60854931008e-06\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"\n",
"#variable Declaration\n",
"\n",
"f1 = 60 # frequency in Hz\n",
"omega1 = 2*pi*f1 # angular frequency in Hz\n",
"f2 = 100 # frequency in MHz\n",
"f2 = 100*10**6 # frequency in Hz\n",
"omega2 = 2*pi*f2 # angular frequency in Hz\n",
"sigma = 5.8*10**7 # conductivity in mho/m\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"epsilon_r = 1 # relative permittivity\n",
"mu_r = 1 # relative permeability\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu = mu_0*mu_r # permeability\n",
"\n",
"print \"At f = 60Hz\"\n",
"k1 = (sigma)/(omega1*epsilon) # ratio\n",
"print \"ratio k is equal to\",k1\n",
"print \"since k>>1 therefore it is very good conductor at f = 60Hz:\"\n",
"delta1 = (sqrt(2/(omega1*mu*sigma))) # depth of penetration in m\n",
"print \"depth of penetration delta1 in m:\",delta1\n",
"\n",
"print \"At f = 100Hz\"\n",
"k2 = sigma/(omega2*epsilon) # ratio\n",
"print \"ratio k is equal to\",k2\n",
"print \"since k2>>1 therefore it is very good conductor at f = 100Hz:\"\n",
"delta2 = (sqrt(2/(omega2*mu*sigma))) # depth of penetration in m\n",
"print \"depth of penetration delta2 in m:\",delta2\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.23,Page Number 121"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"when f = 1MHz\n",
"displacement current when f = 1MHz in A: 9.59160736375e-12\n",
"when f = 100MHz\n",
"displacement current when f = 100MHz in A: 9.59160736375e-10\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"\n",
"#variable Declaration\n",
"\n",
"Ic = 10 # conduction current in ampere\n",
"epsilon_r = 1 # relative permittivity\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"sigma = 5.8*10**7 # conductivity in mho/m\n",
"\n",
"print \"when f = 1MHz\"\n",
"f = 1 # frequency in MHz\n",
"f = 1*10**6 # frequency in Hz\n",
"Id = (2*pi*f*epsilon*Ic)/sigma # printlacement current\n",
"print \"displacement current when f = 1MHz in A:\",Id\n",
"print \"when f = 100MHz\"\n",
"f = 100 # frequency in MHz\n",
"f = 100*10**6 # frequency in Hz\n",
"Id = (2*pi*f*epsilon*Ic)/sigma # printlacement current\n",
"print \"displacement current when f = 100MHz in A:\",Id\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.25,Page Number 122"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ratio k is equal to:\n",
"ratio: 221.92\n",
"K is >>1 so sea water is a good conductor\n",
"depth in the sea that can be reached by the aeroplane in m: 1.41095\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin,cos,radians,log\n",
"\n",
"#variable declaration\n",
"Em = 20 # minimum signal level required for vessel under sea water in microV/m\n",
"Em = 20*10**-6 # minimum signal level required for vessel under sea water in V/m\n",
"E = 100 # electric intensity of wave in V/m\n",
"v = 3*10**8 # speed of light in m/s\n",
"f = 4 # frequency in MHz\n",
"f = 4*10**6 # frequency in Hz\n",
"omega = 2*pi*f # angular frequency in Hz\n",
"sigma = 4 # conductivity of sea water in mho/m\n",
"epsilon_r = 81 # relative permittivity\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu_r = 1 # relative permeability\n",
"mu_0 = 4*pi*10**(-7) # permeability in free space\n",
"mu = mu_r*mu_0 # permeability\n",
"k = (sigma)/(omega*epsilon) #ratio\n",
"print \"ratio k is equal to:\"\n",
"print \"ratio:\",round(k,3)\n",
"print \"K is >>1 so sea water is a good conductor\"\n",
"eta_1 = 377 # intrinsic impedance in free space in ohm\n",
"alpha_1 = 0 # attenuation constant in free space in m**-1\n",
"\n",
"\n",
"#calculations\n",
"beta_1 = omega/v # phase constant in m**-1\n",
"mageta_2 = sqrt((omega*mu)/sigma) # magnitude of eta_2(intrinsic impedance of sea water in ohm) \n",
"argeta_2 = 45 # argument of eta_2 in degrees\n",
"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))\n",
"TC = 2*eta_2/(eta_1+eta_2) # transmission cofficient\n",
"Et = abs(TC)*E # transmitted electric field in V/m\n",
"alpha_2 = sqrt((omega*mu*sigma)/2) # attenuation constant for sea water in m**-1\n",
"# formula: Et*exp(-alpha_2*d) = Em\n",
"d = -(1/alpha_2)*(log(Em/Et)) # depth in the sea that can be reached by the aeroplane in m\n",
"\n",
"\n",
"#result\n",
"print \"depth in the sea that can be reached by the aeroplane in m:\",round(d,5)\n",
"\n",
"\n",
"# note 1: the value of alpha_2 in book is 7.905 but it is \"7.94\" exactly calculated by python.\n",
"#note 2 : The correct answer of the Depth(d) is \"1.41095\" the answer in the book is wrong.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.27,Page Number 124"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"E=sin(omega*t-beta*z)ax+2*sin(omega*t-beta*z+75)ay # electric field in V/m\n",
"power per unit area conveyed by the wave in free space in mW/m**2: 6.631\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt\n",
"\n",
"#variable declaration\n",
"\n",
"eta_0=377 # intrinsic impedance in free space in ohm\n",
"print \"E=sin(omega*t-beta*z)ax+2*sin(omega*t-beta*z+75)ay # electric field in V/m\"\n",
"Ex=1 # magnitude of Ex\n",
"Ey=2 # magnitude of Ey\n",
"\n",
"#calculations\n",
"E=sqrt(Ex**2+Ey**2) # resultant magnitude\n",
"Pav=((1/2)*E**2)/(eta_0) # power per unit area conveyed by the wave in free space\n",
"\n",
"#results\n",
"print \"power per unit area conveyed by the wave in free space in mW/m**2:\",round(Pav*1000,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.28,Page Number 125"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average power in micro*w/m**2: 2354.59\n",
"maximum energy density of the wave in PJ/m*3: 31.416\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"#variable declaration\n",
"\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"epsilon_r = 4 # relative permittivity\n",
"mu_r = 1 # relative permeability\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu = mu_0*mu_r # permeability\n",
"H = 5 # magnitude of magnetic field in mA/m\n",
"H = 5*10**-3 # magnitude of magnetic field in A/m\n",
"\n",
"#calculations\n",
"eta = sqrt(mu/epsilon) # intrinsic impedence in ohm\n",
"E = H*sqrt(mu/epsilon) # magnitude of electric field\n",
"P_av = E**2/(2*eta) # average power\n",
"W_E = epsilon*E**2 # maximum energy density of the wave\n",
"\n",
"\n",
"#results\n",
"print \"Average power in micro*w/m**2:\",round(P_av*10**6,2)\n",
"print \"maximum energy density of the wave in PJ/m*3:\",round(W_E*10**12,3)\n",
"\n",
"\n",
"#note: P_av is = 2353.75 in book but it is 2354.58 correctly calculated by python.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.29,Page Number 125"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"electric energy density of the wave in nJ/m**3: 139.078\n",
"magnetic energy density of wave in nJ/m**3: 139.078\n",
"Total energy density in nJ/m**3: 278.157\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"#variable declaration\n",
"\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"epsilon_r = 1 # relative permittivity\n",
"mu_r = 1 # relative permeability\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu = mu_0*mu_r # permeability\n",
"E = 100*sqrt(pi) # magnitude of electric field in V/m\n",
"\n",
"\n",
"#calculations\n",
"W_E = (1/2)*epsilon*E**2 # electric energy density of the wave\n",
"W_H = W_E # as the energy density is equal to that of magnetic field for a pla`ne travelling wave\n",
"W_T = W_E+W_H # total energy density\n",
"\n",
"#results\n",
"print \"electric energy density of the wave in nJ/m**3:\",round(W_E*10**9,3)\n",
"print \"magnetic energy density of wave in nJ/m**3:\",round(W_H*10**9,3)\n",
"print \"Total energy density in nJ/m**3:\",round(W_T*10**9,3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.30,Page Number 126"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"when frequency = 25kHz\n",
"transmitted distance in m: 3.274\n",
"when frequency = 25MHz\n",
"transmitted distance in m: 0.105\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi\n",
"\n",
"#variable Declaration\n",
"\n",
"sigma = 5 # conductivity of sea water in mho/m\n",
"f1 = 25 # frequency in kHz\n",
"f1 = 25*10**3 # frequency in Hz\n",
"omega1 = 2*pi*f1 # angular frequency in Hz\n",
"f2 = 25 # frequency in MHz\n",
"f2 = 25*10**6 # frequency in Hz\n",
"omega2 = 2*pi*f2 # angular frequency in Hz\n",
"epsilon_r = 81 # relative permittivity\n",
"epsilon_0 = 8.854*10**(-12) # permittivity in free space\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu_r = 1 # relative permeability\n",
"mu_0 = 4*pi*10**(-7) # permeability in free space\n",
"mu = mu_r*mu_0 # permeability\n",
"\n",
"#calculations and results\n",
"\n",
"print \"when frequency = 25kHz\"\n",
"alpha_1 = omega1*sqrt((mu*epsilon)/2*(sqrt(1+(sigma**2/(omega1**2*epsilon**2)))-1)) # attenuation constant when f = 25kHz\n",
"# formula: exp(-alpha*x) = 0.1\n",
"x1 = 2.3/alpha_1 # transmitted distance in m\n",
"print \"transmitted distance in m:\",round(x1,3)\n",
"print \"when frequency = 25MHz\"\n",
"alpha_2 = omega2*sqrt((mu*epsilon)/2*(sqrt(1+(sigma**2/(omega2**2*epsilon**2)))-1)) # attenuation constant when f = 25MHz\n",
"x2 = 2.3/alpha_2 # transmitted distance in m\n",
"print \"transmitted distance in m:\",round(x2,3)\n",
"\n",
"\n",
"# note: the values of epsilon_r = 81 and of mu_r = 1 for sea water which are not given in the book.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.31,Page Number 126"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"reflection cofficient of electric field in mV/m: 0.489\n",
"incident cofficient of magnetic field in micro*A/m: 7.739\n",
"reflection cofficient of magnetic field in micro*A/m: 3.786\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,radians,asin,cos,sin,degrees\n",
"\n",
"#variable Declaration\n",
"\n",
"E_i = 1 # magnitude of incident electric field in mV/m\n",
"E_i = 1*10**-3 # magnitude of incident electric field in V/m\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"theta_i = 15 # incident angle in degrees\n",
"epsilon_r1 = 8.5 # relative permittivity of medium 1\n",
"mu_r1 = 1 # relative permeability of medium 1\n",
"epsilon1 = epsilon_r1*epsilon_0 # permittivity\n",
"mu1 = mu_0*mu_r1 # permeability\n",
"eta1 = sqrt(mu1/epsilon1) # intrinsic impedence of medium 1 in ohm\n",
"epsilon2 = epsilon_0 # permittivity of medium 2\n",
"mu2 = mu_0 # permeability of medium 2\n",
"eta2 = sqrt(mu2/epsilon2) # intrinsic impedence of medium 2 in ohm\n",
"\n",
"#calculations and result\n",
"\n",
"# formula : sin(theta_i)/sin(theta_t) = sqrt(epsilon2/epsilon1)\n",
"theta_t = asin(sin(radians(theta_i)))/(sqrt(epsilon2/epsilon1)) # transmitted angle in degrees\n",
"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\n",
"print \"reflection cofficient of electric field in mV/m:\",round(E_r*1000,3)\n",
"H_i = E_i/eta1 # incident cofficient of magnetic field\n",
"print \"incident cofficient of magnetic field in micro*A/m:\",round(H_i*10**6,3)\n",
"H_r = E_r/eta1 # reflection cofficient of electric field\n",
"print \"reflection cofficient of magnetic field in micro*A/m:\",round(H_r*10**6,3)\n",
"\n",
"\n",
"#note : minute difference in decimel in the value of H_i and H_r.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 2.32,Page Number 127"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"average power density absorbed by copper in mW/m**2: 3.83\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import pi,sqrt\n",
"\n",
"#variable declaration\n",
"\n",
"sigma = 5.8*10**7 # conductivity in mho/m\n",
"f = 2 # frequency in MHz\n",
"f = 2*10**6 # frequency in Hz\n",
"omega = 2*pi*f # angular frequency in rad/sec\n",
"E = 2 # magnitude of electric field in mV/m\n",
"E = 2*10**-3 # magnitude of electric field in V/m\n",
"epsilon_0 = 8.854*10**-12 # permittivity in free space in F/m\n",
"mu_0 = 4*pi*10**-7 # permeability in free space in H/m\n",
"epsilon_r = 1 # relative permittivity\n",
"mu_r = 1 # relative permeability\n",
"epsilon = epsilon_r*epsilon_0 # permittivity\n",
"mu = mu_0*mu_r # permeability\n",
"\n",
"# calculations\n",
"eta = sqrt(mu*omega/sigma) # intrinsic impedence in ohm\n",
"P_av = (1/2)*E**2/eta # average power density anbsorbed by copper\n",
"\n",
"#result\n",
"print \"average power density absorbed by copper in mW/m**2:\",round(P_av*1000,2)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 0
}