G = 70%-90% VG = 90%-
There are few strategies to earn VG:
a) ignoring extra points and focussing on oral exam and project (45%+45%)
b) using extra points to fill in to VG (35% from oral + 35% from project
+ 20% extra points)
c) if you are on the border to get VG (being VG candidate) you
can fill in to VG by using extra points
Example: You are nervous at the oral exam and you get only 20% (which is very unlikely if you have prepared well). Anyway, since you were working hard, you have probably got 30% from (2), and 20% from (3). Note that you pass (you've got your 70%), but you also have a chance to get VG by knowing four chapters marked by VG which brings you extra 5x4%=20%. So you've got 90% in total, thus VG.
G = 70%-90% VG = 90%-
Below follows list of concepts you should comfortably operate with. This means that on the oral exam you will be expected to enter in discussion using concepts which are listed below. Few remarks:
Before going on some bird's eye view of the course:Concepts are implemented in the list of chapters from Grant & Philips book ("Electro-magnetism" , Willey & Sons, 2000). After name of the chapeter/section/subsection, list of the concepts it coveres is given in italic. Also, any other comments related to chapter/section/subsection will be given in italic. Naturally, you can use any other book which is on the same level as Grant & Philips. However, make sure that you cover list of concepts listed below. Some sections/subsections are not included as requirements. In such case their name is listed in bold italic. However, it is still possible that you will be asked about the concepts from chapters like that. Could be that you just have to understand certain formua etc.. Such cases will be commented in italic. If chapter is omitted (marked in bold italic) and marked with VG you have to know it to earn VG. In other words, on the oral exam, you might be asked question related to this chapter. Some chapters are omited completely: chapters 9, 12, 13, 14 do not appear on the list.
We have followed the book closely, thus we have followed historical path of deriving Maxwell's equations (which are the heart of the course). All electrostatics and magnetostatics has surved the purpose of `deriving' 4 laws:
(1) Gauss Law: div E = rho/eps0
(2a) E is conservative field: curl E = 0 -> (2b) curl E = -dB/dt (Faraday's
law)
(3) Ampere's law: 1/mu_0 curl B = j
(4) Absense of magnetic monopoles (no sources or sinks of B field):
div B = 0
(1) and (2a) deal with electrostatics and we have studied them in vacuum and in the presence of materials. (3) and (4) deal with magnetic effects. (2b) was studied at the end (after 1,2a,3,4)since it combines electrical and magnetic phenomena. Two other important topics which are not directly related to Maxwell's equations were (5) metals (which are special in a sense that they screen all field from outside) and (6) circuits (having to do with Ohm's law which describes behavior of simples element, to more complicated behavior of coil U=-LdI/dt, etc.). Connnected to (6) is usage of complex notation in describing circiuits with alternating currents.
Should you be able to understand theory or do calculations or both? Ideally you should be able to do both (that's kind of obvious). The oral exam will assess your understanding of theory and it is possible that you will have to prove your calculations skills by manipulating some equations to strengthten your arguments during discussion. During the second written `extra point ' exam you had a chance to show your calculational skills (plug one equation into another, set up the problem properly, etc.). You are problem solvers: meaning that goal of the course is to give you tools and training to solve problems related to electromagnetism. This implies quite technical steps (like in the project you have to do, proving that you can deal with real world scinece problems) and less technical steps (see where the problem is how to attack puzzle, looking for clues, connecting various concepts) which you could practise on written first `extra point' exam.
Here are details:
1 FORCE AND ENERGY IN ELECTROSTATICS [Coulomb's law, Gauss' law, electric field and potential, energy of group of charges - two ways to calculate it etigher by considering amount of work needed to put it together (eq. 1.36) or take E^2 and integrate it out of the whole space where field is not zero (eq.1.42). Flux of field through the surface is another important topic you should be able to explain why flux is given by EdScos(theta) and not only EdS]
1.1 Electric Charge - 2 [Coulomb's law, superposition of forces, what is charge, what determines unit of charge, radial character of force between two point charges]2 DIELECTRICS [In contract to chapter 1 which deals with vaccum, here the emphasis is on materials. You should have understanding of relative permittivity \epsilon and electric susceptibility \xi which describe electrostatic properties of materials. This is one of the hardest topics in the course. Main message is that if you have polarized dielectric then you can think of it as object having surface charge density (given by eq.2.3) and volume charge density (given by eq.2.17). Another emphasis is how to actually calcuate \epsilon if you know polarizability of the molecule. Problem is that \epsilon in 2.5 connects macroscopic quantities while polarizability referes to microscipic quantities. This is the reason why one has to work with E_local and E separately. There are two mechanisms which induce dipole moment. If molecule does not have permanent dipole moment it can be induced (section 2.2.3). Second mechanism is for molecules which have permanent dipole moment, then it is important to orient them in proper way (section 2.2.2)]
1.2 The Electric Field - 6 [ purpose of the test charge, superposition of electric field, positive and negative point charges as source and sink of electric field]
1.3 Electric Fields in Matter - 10
1.3.1 The Atomic Charge Density - 10 [charge density - what's wrong with it?, what's right with it - why is it useful?]
1.3.2 The Atomic Electric Field - 11 [remember oversimplified model of the atom at the problem solving class, the point is that field dies out very fast when moving away from the atom, however, close to the atom and in the atom it is very strong]
1.3.3 The Macroscopic Electric Field - 13 [average field - contrast it with atomic field, definition of metal, meaning of surcae charge density - it is idealization but still makes sense when one is not too close to the surface]
1.4 Gauss' Law - 16 [one of the key topics]
1.4.1 The Flux of a Vector Field - 17 [meaning of the flux, scalar produc of the field and surface element is crucial - the importance of the cos(theta) factor]
1.4.2 The Flux of the Electric Field out of a Closed Surface - 19 [solid angle, cancelation of r^2 from the surcae element with r^2 in the expression for the electric field makes Gauss' law possible, field close to the plane which carries surface charge]
1.4.3 The Divergence of a Vector Field - 24 [meaning of div E]
1.4.4 The Differential Form of Gauss' Law - 26 [one of the key topics]
1.5 Electrostatic Energy - 28 [who does the work and who receives the work, meaning of "-" sign in potential enetry differential dE=-Fdx ]
1.5.1 The Electrostatic Potential - 28 [role of the test charge]
1.5.2 The Electric Field as the Gradient of the Potential - 31
1.5.3 The Dipole Potential - 35 [one of the key topics, why it dies faster then potential from point charge]
1.5.4 Energy Changes Associated with the Atomic Field - 38 [You have to be familiar with Eq. 1.36: it is very important equations explaining energetics of group of charges. It tells you what is the amount of work you have to do in order to build up this charge distribution. This quantity is marked with U and is actually potential energy of group of charges]
1.5.5 Capacitors, and Energy in Macroscopic Fields - 40 [pay attention to Eq. 1.42. since this is important equation, it tells you that you can calculate energy needed to assemble certain charge distribution by integrating square of the electric field being generated by this charge distribution]
1.5.6 Energy Stored by a Number of Charged Conductors - 44
PROBLEMS 1 - 46
2.1 Polarization 49 [polarization vector as average of induced atomic dipole moments; Dielectrics do not have free electrons (thus being very different from metals) - atoms which make dielectric are basically neutral. If extrenal field is applied only electron cloud is reshaped which gives rise to induced dipole moment, thus polarization of the atom. Charge density induced on the surface of the dielectric figure 2.2]3 ELECTROSTATIC FIELD CALCULATIONS [image method]
2.2 Relative Permittivity and Electric Susceptibility 55 [Polarization vector is proportional to E field established in the material]
2.2.1 The Local Field 59 (You are not expected to discuss in detail concept of local field, though should have rough understanding what the whole thing is about - where the problem is. Also, you should be able to explain what polarizability of the molecule is.)
2.2.2 Polar Molecules 60 (You have to be familiar with Eq. 2.11. It is very important equation telling you about energetics of electric dipole in presence of electric field.)
2.2.3 Non-polar Liquids 67
2.3 Macroscopic Fields in Dielectrics 70
2.3.1 The Volume Density of Polarization Charge. 71 [If polarization vector is non uniform there will be induced charge density in dielectric, you should have understanding of formula 2.17]
2.3.2 The Electric Displacement Vector. 73 [induced charge density has to be added to Gauss's law, and E field has to be modified into the D field]
2.3.3 Boundary Conditions for D and E. 76 [one of the key topics]
2.4 Energy in the Presence of Dielectrics 79
2.4.1- Some Further Remarks about Energy and Forces. 80
PROBLEMS 2 - 82
3.1 Poisson's Equation and Laplace's Equation - 854 STEADY CURRENTS AND MAGNETIC FIELDS [similar in spirit to chapter 1, the only difference is that source of the B field is moving charge, Lorentz force, Hall effect, magnetic dipole, torque on magnetic dipole in external magnetic field, Ampere's law in intergral and diffrential form. Biot-Savart law. Ohm's law, conductivity, how come that E is not equal 0 in metal when baterry is connected to metal to form the circuit? The magnetic vector potential A]
3.1.1 The Uniqueness Theorem 88 [you just have to know that solution to Lapl and Pois eq. is unique if boundary conditions are specified]
3.1.2 Electric Fields in the Presence of Free Charge 89
3.2 Boundaries Between Different Regions 91
3.3 Boundary Conditions and Field Patterns - 93
3.3.1 Electrostatic Images - 93
3.3.2 Spheres and Spherical Cavities in Uniform External Field 97 [you should be familiar with fig 3.6]
3.4 Electrostatic Lenses - 100
3.5 Numerical Solutions of Poisson's Equation. 103
3.6 Summary of Electrostatics. 107
PROBLEMS 3 -109
4.1 Electromotive Force and Conduction. ..1125 MAGNETIC MATERIALS [same as chapter 4 but not in vacuum, magnetic susceptibility, relative permeability, H field]
4.1.1 Current and Resistance. .112 [Ohm's law -eq. 4.4]
4.1.2 The Calculation of Resistance. 116
4.2 The Magnetic Field 119
4.2.1 The Lorentz Force 119
4.2.2 Magnetic Field Lines 123 [absence of magnetic monopoles - no sources or sinks for B]
4.3 The Magnetic Dipole 127
4.3.1 Current. Loops in External Fields 127
4.3.2 MagnetIc Dipoles and Magnetic Fields 130
4.4 Ampere's Law 132
4.4.1 The Field of a Large Current Loop 132 (You should know and have understanding of Eq. 4.31, the Ampere's Law. The derivation of this equation is a bit too blurry. Though, the equation itself can be understood. Furthermore it is very important equation and you should know it.)
4.4.2 The Biot-Savart Law 137
4.4.3 Examples of the Calculation of Magnetic Fields 139 (Here you should be familiar with all examples)
4.5 The Differential Form of Ampere's Law 144
4.5.1 The Operator Curl 144
4.5.2 The Vector Curl B 148
4.5.3 The Magnetic Vector Potential 148
4.6 Forces and Torques on Coils 150
4.6.1Magnetic Flux 151
4.7 The Motion of Charged Particles in Electric and Magnetic Fields. 154
4.7.1 The Motion of a Charged Particle in a Uniform Magnetic Field. 155
4.7.2 Magnetic Mirrors and Plasmas. 157
4.7.3 Magnetic Quadrupole Lenses. 159
PROBLEMS 4 - 163
5.1 Magnetization. ..166 [analog of polarization]6 ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY [Faraday's law, Lenz's law, self induction, mutual induction, energy of magnetic field]
5.1.1 Diamagnetism. 169 [mechanism how magnetization is induced in such material - no permanent magnetic dipole moment]
5.1.2 Paramagnetism. 173 [permanent magnetic dipole moment]
5.1.3 Ferromagnetism .175 [domains of ordered magnetic dipoles, Currie temperature]
5.2 The Macroscopic Magnetic Field Inside Media. 176 [magnetion induces volume and surface current densities]
5.2.1 The Surface Currents on a Uniformly Magnetized Body. 178
5.2.2 The Distributed Currents Within a Magnetized Body. 179
5.2.3 Magnetic Susceptibility and Atomic Structure. 183
5.3 The Field Vector H ..186
5.3.1 Ampere's Law for the Field H .186
5.3.2 The Boundary Conditions on the Field Band H ..191
5.4 Magnets - 194
5.4.1 Electromagnets - 194 [how to map magnetic circuit onto the electrical one eq. 5.45, hysteresis curve - fig 5.19, nonlinear effects]
5.4.2 Permanent Magnets - 204
5.5 Summary of Magnetostatics - 208
PROBLEMS 5 - 209
6.1 Electromagnetic Induction - 2127 ALTERNATING CURRENTS AND TRANSIENTS [there is differentce in behavior of the circuit when oscillating voltage is applied all the time and when constant voltage is applied and then switched off or vice versa, you should be familiar with complex notation]
6.1.1 Motional Electromotive Force - 214
6.1.2 Faraday's Law - 218
6.1.3 Examples of Induction - 221
6.1.4 The Differential Form of Faraday's Law - 228
6.2 Self-inductance and Mutual Inductance - 230
6.2.1 Self-inductance - 230
6.2.2 Mutual Inductance - 232
6.3 Energy and Forces in Magnetic Fields. 234
6.3.1The Magnetic Energy Stored in an Inductor. .234
6.3.2 The Total Magnetic Energy of a System of Currents. 235
6.3.3 The Potential Energy of a Coil in a Field and the Force
6.3.4 The Total Magnetic Energy in Terms of the Fields B and H .239
6.3.5 Non-linear Media. .241
6.3.6 Further Comments on Energy in Magnetic Fields. .243
6.4 The Measurement of Magnetic Fields and Susceptibilities. 246 [VG]
6.4.1 The Measurement of Magnetic Fields - 246 [VG]
6.4.2 The Measurement of Magnetic Susceptibilities - 248 [VG]
PROBLEMS 6 - 250
7.1 Alternating Current Generators. .2538 LINEAR CIRCUITS
7.2 Amplitude, Phase and Period. .256
7.3 Resistance, Capacitance and Inductance in A.C. Circuits. .257
7.4 The Phase Diagram and Complex Impedance. 260
7.5 Power in A.C. Circuits. 266
7.6 Resonance. .268 [one of the key topics]
7.7 Transients. .274
PROBLEMS 7 .280
8.1 Networks. .282
8.1.1 Kirchhoffs Rules ..283
8.1.2 Loop Analysis, Node Analysis and Superposition. .286
8.1.3 A.C. Networks. 288
8.2 Audio-frequency Bridges. .291
8.3 Impedance and Admittance. 293
8.3.1 Input Impedance. .296
8.3.2 Output Impedance and Thevenin's Theorem. .297
8.4 Filters. 299
8.4.1 Ladder Networks. .301
8.4.2 Higher Order Filters and Delay Lines. 303
8.5 Transformers. .307 [Beautifull application of Faraday's law in real life]
8.5.1 The Ideal Transformer. .308
8.5.2 Applications of Transformers. .311
8.5.3 Real Transformers. .312
PROBLEMS 8 - 318
10 MAXWELL'S EQUATIONS [Heart of the whole book and the course.
The point is that electrostatic and magnetostatic laws have to be extenced
to time dependent situations - a tedious task acomplished by Maxwell. He
derived set of equations, which you should understand and be able to "derive"
from static laws. After you are familiar with Gauss' law, Ampere's law,
and Faraday's law the only non-trivial thing is to understand how to bring
in Displacement current in Ampere's law]
10.1 The Equation of Continuity. .34811 ELECTROMAGNETIC WAVES [Once Maxwell's equations are given they can be used to predict properties of the time dependent systems (withing the framework of electromagnetism, naturally). One of the most important `predictions' is that speed of light can be calculated from \epsilon_0 and \mu_0 giving a proof that light is a electromagnetic wave.]
10.2 Displacement Current. 350
10.3 Maxwell's Equations. 356
10.4 Electromagnetic Radiation. 359
10.5 The Microscopic Field Equations - 360
PROBLEMS 10 - 362
11.1 Electromagnetic Waves in Free Space. .365 [derivation of wave equation from Maxwell's equation, discussion of special solution to wave equation]APPENDIX A UNITS
11.2 Plane Waves and Polarization. 368 [another special solution to wave equation]
11.2.1 Plane Waves in Free Space .373
11.2.2 Plane Waves in Isotropic Insulating Media. 375
11.3 Dispersion. 379
11.4 Energy in Electromagnetic Waves. .383 [you should understand equation 11.33, be able to argue what it represents]
11.5 The Absorption of Plane Waves in Conductors and the Skin Effect. 388 [Ohm's law + Maxwell equations]
11.6 The Reflection and Transmission of Electromagnetic Waves - 391
11.6.1 Boundary Conditions on Electric and Magnetic Fields - 392
11.6.2 Reflection at Dielectric Boundaries - 396
11.6.3 Reflection at Metallic Boundaries - 399
11.6.4 Polarization by Reflection - 401
11.7 Electromagnetic Waves and Photons. 404 [VG]
PROBLEMS 11 - 406
A.1 Electrical Units and Standards. 477APPENDIX B FIELDS AND DIFFERENTIAL OPERATORS
A.1.1 The Definition of the Ampere. 477
A.I.2 Calibration and Comparison of Electrical. Standards. .479
A.2 Gaussian Units. 482
A.3 Conversion between SI and Gaussian Units. .485
B.1 The Operators div, grad and curl. .487APPENDIX C THE DERIVATION OF THE BIOT-SAVART LAW
B.2 Formulae in Different Coordinate Systems. .489
B.3 Identities. 493
1 FORCE AND ENERGY IN ELECTROSTATICS
1.1 Electric Charge.2 DIELECTRICS
1.2 The Electric Field
1.3 Electric Fields in Matter - 10
1.3.1 The Atomic Charge Density - 10
1.3.2 The Atomic Electric Field
1.3.3 The Macroscopic Electric Field - 13
1.4 Gauss' Law - 16
1.4.1 The Flux of a Vector Field - 17
1.4.2 The Flux of the Electric Field out of a Closed Surface - 19
1.4.3 The Divergence of a Vector Field - 24
1.4.4 The Differential Form of Gauss' Law - 26
1.5 Electrostatic Energy - 28
1.5.1 The Electrostatic Potential - 28
1.5.2 The Electric Field as the Gradient of the Potential - 31
1.5.3 The Dipole Potential - 35
1.5.4 Energy Changes Associated with the Atomic Field - 38 (You have to be familiar with Eq. 1.36: it is very important equations explaining energetics of group of charges. It tells you what is the amount of work you have to do in order to build up this charge distribution. This quantity is marked with U and is actually potential energy of group of charges)
1.5.5 Capacitors, and Energy in Macroscopic Fields - 40 (pay attention to Eq. 1.42. since this is important equation, it tells you that you can calculate energy needed to assemble certain charge distribution by integrating square of the electric field being generated by this charge distribution)
1.5.6 Energy Stored by a Number of Charged Conductors - 44
PROBLEMS 1 - 46
2.1 Polarization 493 ELECTROSTATIC FIELD CALCULATIONS
2.2 Relative Permittivity and Electric Susceptibility 55
2.2.1 The Local Field 59 (You are not expected to discuss in detail concept of local field, though should have rough understanding what the whole thing is about - where the problem is. Also, you should be able to explain what polarizability of the molecule is.)
2.2.2 Polar Molecules 60 (You have to be familiar with Eq. 2.11. It is very important equation telling you about energetics of electric dipole in presence of electric field.)
2.2.3 Non-polar Liquids 67
2.3 Macroscopic Fields in Dielectrics 70
2.3.1 The Volume Density of Polarization Charge. 71
2.3.2 The Electric Displacement Vector. 73
2.3.3 Boundary Conditions for D and E. 76
2.4 Energy in the Presence of Dielectrics 79
2.4.1- Some Further Remarks about Energy and Forces. 80
PROBLEMS 2 - 82
3.1 Poisson's Equation and Laplace's Equation - 854 STEADY CURRENTS AND MAGNETIC FIELDS
3.1.1 The Uniqueness Theorem 88
3.1.2 Electric Fields in the Presence of Free Charge 89
3.2 Boundaries Between Different Regions 91
3.3 Boundary Conditions and Field Patterns - 93
3.3.1 Electrostatic Images - 93
3.3.2 Spheres and Spherical Cavities in Uniform External Field 97
3.4 Electrostatic Lenses - 100
3.5 Numerical Solutions of Poisson's Equation. 103
3.6 Summary of Electrostatics. 107
PROBLEMS 3 -109
4.1 Electromotive Force and Conduction. ..1125 MAGNETIC MATERIALS
4.1.1 Current and Resistance. .112
4.1.2 The Calculation of Resistance. 116
4.2 The Magnetic Field 119
4.2.1 The Lorentz Force 119
4.2.2 Magnetic Field Lines 123
4.3 The Magnetic Dipole 127
4.3.1 Current. Loops in External Fields 127
4.3.2 MagnetIc Dipoles and Magnetic Fields 130
4.4 Ampere's Law 132
4.4.1 The Field of a Large Current Loop 132 (You should know and have understanding of Eq. 4.31, the Ampere's Law. The derivation of this equation is a bit too blurry. Though, the equation itself can be understood. Furthermore it is very important equation and you should know it.)
4.4.2 The Biot-Savart Law 137
4.4.3 Examples of the Calculation of Magnetic Fields 139 (Here you should be familiar with all examples)
4.5 The Differential Form of Ampere's Law 144
4.5.1 The Operator Curl 144
4.5.2 The Vector Curl B 148
4.5.3 The Magnetic Vector Potential 148
4.6 Forces and Torques on Coils 150
4.6.1Magnetic Flux 151
4.7 The Motion of Charged Particles in Electric and Magnetic Fields. 154
4.7.1 The Motion of a Charged Particle in a Uniform Magnetic Field. 155
4.7.2 Magnetic Mirrors and Plasmas. 157
4.7.3 Magnetic Quadrupole Lenses. 159
PROBLEMS 4 - 163
5.1 Magnetization. ..166I have stopped here. I will go through the rest soon as I have more grasp on your interests and understanding. Still, if you want to learn ahead of time, then you have hard copies to give you rough ideas what will be omitted.
5.1.1 Diamagnetism. 169
5.1.2 Paramagnetism. 173
5.1.3 Ferromagnetism .175
5.2 The Macroscopic Magnetic Field Inside Media. 176
5.2.1 The Surface Currents on a Uniformly Magnetized Body. 178
5.2.2 The Distributed Currents Within a Magnetized Body. 179
5.2.3 Magnetic Susceptibility and Atomic Structure. 183
5.3 The Field Vector H ..186
5.3.1 Ampere's Law for the Field H .186
5.3.2 The Boundary Conditions on the Field Band H ..191
5.4 Magnets - 194
5.4.1 Electromagnets - 194
5.4.2 Permanent Magnets - 204
5.5 Summary of Magnetostatics - 208
PROBLEMS 5 - 209
6 ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY
6.1 Electromagnetic Induction - 212
6.1.1 Motional Electromotive Force - 214
6.1.2 Faraday's Law - 218
6.1.3 Examples of Induction - 221
6.1.4 The Differential Form of Faraday's Law - 228
6.2 Self-inductance and Mutual Inductance - 230
6.2.1 Self-inductance - 230
6.2.2 Mutual Inductance - 232
6.3 Energy and Forces in Magnetic Fields. 234
6.3.1The Magnetic Energy Stored in an Inductor. .234
6.3.2 The Total Magnetic Energy of a System of Currents. 235
6.3.3 The Potential Energy of a Coil in a Field and the Force
6.3.4 The Total Magnetic Energy in Terms of the Fields B and H .239
6.3.5 Non-linear Media. .241
6.3.6 Further Comments on Energy in Magnetic Fields. .243
6.4 The Measurement of Magnetic Fields and Susceptibilities. 246
6.4.1 The Measurement of Magnetic Fields - 246
6.4.2 The Measurement of Magnetic Susceptibilities - 248
PROBLEMS 6 - 250
7 ALTERNATING CURRENTS AND TRANSIENTS
7.1 Alternating Current Generators. .253
7.2 Amplitude, Phase and Period. .256
7.3 Resistance, Capacitance and Inductance in A.C. Circuits. .257
7.4 The Phase Diagram and Complex Impedance. 260
7.5 Power in A.C. Circuits. 266
7.6 Resonance. .268
7.7 Transients. .274
PROBLEMS 7 .280
8 LINEAR CIRCUITS
8.1 Networks. .282
8.1.1 Kirchhoffs Rules ..283
8.1.2 Loop Analysis, Node Analysis and Superposition. .286
8.1.3 A.C. Networks. 288
8.2 Audio-frequency Bridges. .291
8.3 Impedance and Admittance. 293
8.3.1 Input Impedance. .296
8.3.2 Output Impedance and Thevenin's Theorem. .297
8.4 Filters. 299
8.4.1 Ladder Networks. .301
8.4.2 Higher Order Filters and Delay Lines. 303
8.5 Transformers. .307
8.5.1 The Ideal Transformer. .308
8.5.2 Applications of Transformers. .311
8.5.3 Real Transformers. .312
PROBLEMS 8 - 318
10 MAXWELL'S EQUATIONS
10.1 The Equation of Continuity. .34811 ELECTROMAGNETIC WAVES
10.2 Displacement Current. 350
10.3 Maxwell's Equations. 356
10.4- Electromagnetic Radiation. 359
10.5 The Microscopic Field Equations - 360
PROBLEMS 10 - 362
11.1 Electromagnetic Waves in Free Space. .365APPENDIX A UNITS
11.2 Plane Waves and Polarization. 368
11.2.1 Plane Waves in Free Space .373
11.2.2 Plane Waves in Isotropic Insulating Media. 375
11.3 Dispersion. 379
11.4 Energy in Electromagnetic Waves. .383
11.5 The Absorption of Plane Waves in Conductors and the Skin Effect. 388
11.6 The Reflection and Transmission of Electromagnetic Waves - 391
11.6.1 Boundary Conditions on Electric and Magnetic Fields - 392
11.6.2 Reflection at Dielectric Boundaries - 396
11.6.3 Reflection at Metallic Boundaries - 399
11.6.4 Polarization by Reflection - 401
11.7 Electromagnetic Waves and Photons. 404
PROBLEMS 11 - 406
A.1 Electrical Units and Standards. 477APPENDIX B FIELDS AND DIFFERENTIAL OPERATORS
A.1.1 The Definition of the Ampere. 477
A.I.2 Calibration and Comparison of Electrical. Standards. .479
A.2 Gaussian Units. 482
A.3 Conversion between SI and Gaussian Units. .485
B.1 The Operators div, grad and curl. .487APPENDIX C THE DERIVATION OF THE BIOT-SAVART LAW
B.2 Formulae in Different Coordinate Systems. .489
B.3 Identities. 493
Example: You are nervous at the oral exam and you get only 20% (which is very unlikely if you have prepared well). Anyway, since you were working hard, you have probably got 30% from (2), and 20% from (3). Note that you pass (you've got your 70%), but you also have a chance to get VG by knowing four chapers marked by VG which brings you extra 5x4%=20%. So you've got 90% in total, thus VG.
G = 70%-90% VG = 90%-