1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
|
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 11: Electromagnetic Theory"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.1, Page 559"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"H_0 = 1; # Amplitude off field vector,in A/m\n",
"mu_0 = 12.56e-7; # Permeability,in weber/A-m \n",
"eps = 8.85e-12; # Permittivity in free space,in C/N-meter-square\n",
"\n",
"#Calculations\n",
"# From the relation between the amplitude of the field vector E and vector H of an EM wave in free space \n",
"E_0 = H_0*(sqrt(mu_0/eps));\n",
"\n",
"#Result\n",
"print \"The amplitude of field vector E in free space = %5.1f V/m\"%E_0\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The amplitude of field vector E in free space = 376.7 V/m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.2, Page 560"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"E_o = 1e+3; # Amplitude field vector in free space,N/C\n",
"c = 3e+8; # Speed of light,in m/s\n",
"\n",
"#Calculations\n",
"# 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\n",
"B_o = E_o/c;\n",
"\n",
"#Result\n",
"print \"The maximum value of magnetic induction vector = %4.2e weber/A-m\"%B_o\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum value of magnetic induction vector = 3.33e-06 weber/A-m\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.3, Page 560"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"sigma = 5; # Conductivity of the conducting medium, mho/m\n",
"eps_r = 8.85e-12; # Relative electrical permittivity of medium, F/m\n",
"eps_0 = 1; # Electrical permittivity of free space, F/m\n",
"E0 = 250; # Amplitude of applied electric field, V/m\n",
"\n",
"#Calculations\n",
"J = sigma*E0; # Amplitude of conduction current density, A/metre-square\n",
"J_D = eps_r*eps_0*E0*1e+010; # Amplitude of displacement current density, A/metre-square\n",
"omega = sigma/(eps_0*eps_r); # Frequency at which J = J_D\n",
"\n",
"#Results\n",
"print \"The conduction current density = %3dsin(10^10t) A/metre-quare\"%J\n",
"print \"The displacement current density = %5.3fcos(10^10t) A/metre-quare\"%J_D #incorrect answer in the textbook\n",
"print \"The frequency at which J = J_D is %3.1e Hz\"%omega"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The conduction current density = 1250sin(10^10t) A/metre-quare\n",
"The displacement current density = 22.125cos(10^10t) A/metre-quare\n",
"The frequency at which J = J_D is 5.6e+11 Hz\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.8, Page 565"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"P = 1000; # Energy radiated by the lamp, watt\n",
"r = 2; # Distance from the source at which the electric field intensity is given, m\n",
"\n",
"#Calculations\n",
"S = P/(4*pi*r**2); # Magnitude of Poynting vector, W/metre-square\n",
"# As wave imepdence, Z0 = E/H = 377 and H = E/377, so that with E*H = S we have\n",
"E = 377\n",
"E = sqrt(S*E)\n",
"\n",
"#Result\n",
"print \"The average value of the intensity of electric field of radiation = %4.1f V/m\"%(E)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average value of the intensity of electric field of radiation = 86.6 V/m\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.9, Page 566"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"S = 2*4.186/60*1e+04; # Solar constant, J/s/metre-square\n",
"# From the poynting vector S = E*H \n",
"C = 377; # Wave Impedence, ohm\n",
"\n",
"#Calculations\n",
"E = sqrt(S*C); # Electric field of radiation, V/m\n",
"H = E/C; # Magnetic field of radiation, A/m\n",
"E0 = E*sqrt(2); # Amplitude of electric field of radiation, V/m \n",
"H0 = H*sqrt(2); # Amplitude of magnetic field of radiation, A/m\n",
"\n",
"#Results\n",
"print \"The amplitude of electric field of radiation = %6.1f V/m\"%E0 #incorrect answer in the textbook\n",
"print \"The amplitude of magnetic field of radiation = %5.3f V/m\"%H0\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The amplitude of electric field of radiation = 1025.7 V/m\n",
"The amplitude of magnetic field of radiation = 2.721 V/m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.12, Page 569"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"sigma = 3.54e+007; # Electrical conductivity of Al, mho per metre \n",
"mu = 12.56e-007; # Permeability of the medium, weber/A-m\n",
"f = 71.6e+06; # Frequency of the wave, Hz\n",
"\n",
"#Calculations\n",
"omega = 2*pi*f; # Angular frequency of the wave, rad per sec\n",
"delta = sqrt(2/(sigma*mu*omega)); # Skin depth of the EM wave in Al, m\n",
"\n",
"#Result\n",
"print \"The skin depth of an EM-wave in Al = %2.0f micron\"%(delta/1e-06)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The skin depth of an EM-wave in Al = 10 micron\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.14, Page 571"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import *\n",
"\n",
"#Variable declaration\n",
"sigma = 5.; # Electrical conductivity, mho per metre \n",
"mu = 12.56e-007; # Permeability of the medium, weber/A-m\n",
"eps_0 = 8.85e-012; # Electric permittivity of free space, C-square/N-m-square\n",
"\n",
"#Calculations&Results\n",
"eps = 70*eps_0; # Electric permittivity of the medium, C-square/N-m-square\n",
"delta = 2/sigma*sqrt(eps/mu); # The skin depth and attenuation constant of sea water\n",
"print \"The skin depth of an EM-wave in sea water = %6.4f m\"%delta\n",
"Beta = 1/delta; # The attenuation constant of sea water, per metre\n",
"print \"The attenuation constant of the sea water = %6.2f m\"%Beta\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The skin depth of an EM-wave in sea water = 0.0089 m\n",
"The attenuation constant of the sea water = 112.57 m\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}
|
