# Revisiting Physics after 7 years

1. Dec 31, 2007

### nanoWatt

I had posted this in the wrong thread before I believe, so I moved it here.

This is my first post, so I hope I am following the guidelines. I have a bachelors degree in Physics and a minor in math which I completed back in 2000. Back then I was sort of an average student, but I also did laser research in the lab, so I learned about laser crystals and such.

Now, I want to catch back up, and learn electromagnetic physics such as how light propagates through a medium, and it’s electrical and magnetic properties. I want to revisit simple things like simple harmonic motion, since even these are difficult for me to derive after so long.

I went through 4 calculus classes, so I can’t understand why I’m having so much trouble with even simple limits and such. My focus now is to relearn the Maxwell Equations, and to apply them to how light is affected when it goes through clear quartz.

I guess my questions could be summed up as:

1) Do I need to memorize all the “building block” math parts such as the product rule, summations and series, and all the other basic rules of math?
2) Where is a good source on understanding Maxwell Equations? I printed the Wikipedia article, and another one that derives the equations.
3) Is it possible that since I had done them before, I might pick up the stuff more easily than I did? I had some trouble then fully grasping the subject matter.

For some reason I feel so dumb because even with my bachelors I can’t solve simple limits or do more than just the basic factoring of quadratics, or at least I haven’t put enough effort. I don’t have any textbooks anymore, so I don’t really have direction.

My goal eventually will be to go back to school into the Physics Master’s program, but I need to understand the basics. I must not have been all bad to have made a B in Quantum Mechanics for instance. I remember bits and pieces of the Schrödinger equation, which I think described the wave equation of a hydrogen’s electron spinning around an atom.

I will be doing research in the laser lab, and would probably want to focus on how the magnetic field of light can be affected or shifted. So about ½ theoretical calculation and ½ research.

I look forward to anyone’s guidance.

2. Dec 31, 2007

### Astronuc

Staff Emeritus
Two books which immediately come to mind are:

Introduction to Electrodynamics (3rd Edition), David J. Griffiths
https://www.amazon.com/Introduction-Electrodynamics-3rd-David-Griffiths/dp/013805326X

Mathematical Methods in the Physical Sciences (Hardcover), Mary L. Boas
https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269

Griffiths also has a book on QM.

A couple of other books might be worthwhile to consider:

Electromagnetic Theory and Computation
A Topological Approach
http://assets.cambridge.org/97805218/01607/toc/9780521801607_toc.pdf
Series: Mathematical Sciences Research Institute Publications (No. 48)
Paul W. Gross, MSRI, Berkeley
P. Robert Kotiuga, Boston University

Electromagnetic Theory (IEEE Press Series on Electromagnetic Wave Theory) (Hardcover), Julius Adams Stratton
https://www.amazon.com/Electromagnetic-Theory-IEEE-Press-Wave/dp/0470131535/

TOC for Stratton's book - http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470131535,descCd-tableOfContents.html

Preface
CHAPTER I: THE FIELD EQUATIONS.

MAXWELL'S EQUATIONS.
1.1 The Field Vectors.
1.2 Charge and Current.
1.3 Divergence of the Field Vectors.
1.4 Integral Form of the Field Equations.

MACROSCOPIC PROPERTIES OF MATTER.
1.5 The Inductive Capacities c and p.
1.6 Electric and Magnetic Polarization.
1.7 Conducting Media.

UNITS AND DIMENSIONS.
1.8 M.K.S. or Giorgi System.

THE ELECTROMAGNETIC POTENTIALS.
1.9 Vector and Scalar Potentials.
1.10 Conducting Media.
1.11 Hertz Vectors, or Polarization Potentials.
1.12 Complex Field Vectors and Potentials.

BOUNDARY CONDITIONS.
1.13 Discontinuities in the Field Vectors.

COORDINATE SYSTEMS.
1.14 Unitary and Reciprocal Vectors.
1.15 Differential Operators.
1.16 Orthogonal Systems.
1.17 Field Equations in General Orthogonal Coordinates.
1.18 Properties of Some Elementary Systems.

THE FIELD SENSORS.
1.19 Orthogonal Transformations and Their Invariants.
1.20 Elements of Tensor Analysis.
1.21 Space-time Symmetry of the Field Equations.
1.22 The Lorentz Transformation.
1.23 Transformation of the Field Vectors to Moving Systems.

CHAPTER II: STRESS AND ENERGY.

STRESS AND STRAIN IN ELASTIC MEDIA.
2.1 Elastic Stress Tensor.
2.2 Analysis of Strain.
2.3 Elastic Energy and the Relations of Stress to Strain.

ELECTROMAGNETIC FORCES ON CHARGES AND CURRENTS.
2.4 Definition of the Vectors E and B.
2.5 Electromagnetic Stress Tensor in Free Space.
2.6 Electromagnetic Momentum.

2.7 Electrostatic Energy as a Function of Charge Density.
2.8 Electrostatic Energy as a Function of Field Intensity.
2.9 A Theorem on Vector Fields.
2.10 Energy of a Dielectric Body in an Electrostatic Field.
2.11 Thornson's Theorem.
2.12 Earnshaw's Theorem.
2.13 Theorem on the Energy of Uncharged Conductors.

MAGNETOSTATIC ENERGY.
2.14 Magnetic Energy of Stationary Currents.
2.15 Magnetic Energy as a Function of Field Intensity.
2.16 Ferromagnetic Materials.
2.17 Energy of a Magnetic Body in a Magnetostatic Field.
2.18 Potential Energy of a Permanent Magnet.

ENERGY FLOW.
2.19 Poynting's Theorem.
2.20 Complex Poynting Vector.

FORCES ON A DIELECTRIC IN AN ELECTROSTATIC FIELD.
2.21 Body Forces in Fluids.
2.22 Body Forces in Solids.
2.23 The Stress Tensor.
2.24 Surfaces of Discontinuity.
2.25 Electrostriction.
2.26 Force on a Body Immersed in a Fluid.

FORCES IN THE MAGNETOSTATIC FIELD.
2.27 Nonferromagnetic Materials.
2.28 Ferromagnetic Materials.

FORCES IN THE ELECTROMAGNETIC FIELD.
2.29 Force on a Body Immersed in a Fluid.

CHAPTER III: THE ELECTROSTATIC FIELD.
3.1 Equations of Field and Potential.
3.2 Boundary Conditions.

CALCULATION OF THE FIELD FROM THE CHARGE DISTRIBUTION.
3.3 Green's Theorem.
3.4 Integration of Poisson's Equation.
3.5 Behavior at Infinity.
3.6 Coulomb Field.
3.7 Convergence of Integrals.

EXPANSION OF THE POTENTIAL IN SPHERICAL HARMONICS.
3.8 Axial Distributions of Charge.
3.9 The Dipole.
3.10 Axial Multipoles.
3.11 Arbitrary Distributions of Charge.
3.12 General Theory of Multipoles.

DIELECTRIC POLARIZATION.
3.13 Interpretation of the Vectors P and IT.
3.14 Volume Distributions of Charge and Dipole Moment.
3.15 Single-layer Charge Distributions.
3.16 Double-layer Distributions.
3.17 Interpretation of Green's Theorem.
3.18 Images.

BOUNDARY-VALUE PROBLEMS.
3.19 Formulation of Electrostatic Problems.
3.20 Uniqueness of Solution.
3.21 Solution of Laplace's Equation.

PROBLEM OF THE SPHERE.
3.22 Conducting Sphere in Field of a Point Charge
3.23 Dielectric Sphere in Field of a Point Charge
3.24 Sphere in a Parallel Field
3.25 Free Charge on a Conducting Ellipsoid.
3.26 Conducting Ellipsoid in a Parallel Field.
3.27 Dielectric Ellipsoid in a Parallel Field.
3.28 Cavity Definitions of E and D.
3.29 Torque Exerted on an Ellipsoid.

CHAPTER IV: THE MAGNETOSTATIC FIELD.

GENERAL PROPERTIES OF A MAGNETOSTATFIC FIELD.
4.1 Field Equations and the Vector Potential.
4.2 Scalar Potential.
4.3 Poisson's Analysis.

CALCULATION OF THE FIELD OF A CURRENT DISTRIBUTION.
4.4 Biot-Savart Law.
4.5 Expansion of the Vector Potential.
4.6 The Magnetic Dipole.
4.7 Magnetic Shells.

A DIGRESSION ON UNITS AND DIMENSIONS.
4.8 Fundamental Systems.
4.9 Coulomb's Law for Magnetic Matter.

MAGNETIC POLARIZATION.
4.10 Equivalent Current Distributions
4.11 Field of hfagnetized Rods and Spheres

DISCONTINUITIES OF THE VECTORS A AND B.
4.12 Surface Distributions of Current.
4.13 Surface Distributions of Magnetic Moment.

INTEGRATION OF THE EQUATION.
4.14 Vector Analogue of Green's Theorem.
4.15 Application to the Vector Potential.

BOUNDARY-VALUE PROBLEMS.
4.16 Formulation of the Magnetostatic Problem.
4.17 Uniqueness of Solution.

PROBLEM OF THE ELLIPSOID.
4.18 Field of a Uniformly Magnetized Ellipsoid.
4.19 Magnetic Ellipsoid in a Parallel Field.

CYLINDER IN A PARALLEL FIELD.
4.20 Calculation of the Field.
4.21 Force Exerted on the Cylinder.

PROBLEMS.

CHAPTER V: PLANE WAVES IN UNBOUNDED ISOTROPIC MEDIA.

PROPAGATION OF PLANE WAVES.
5.1 Equations of a One-dimensional Field.
5.2 Plane Waves Harmonic in Time.
5.3 Plane Waves Harmonic in Space.
5.4 Polarization.
5.5 Energy Flow.
5.6 Impedance.

GENERAL SOLUTIONS OF THE ONE-DIMENSION WAVE EQUATION.
5.7 Elements of Fourier Analysis.
5.8 General Solution of the One-dimensional Wave Equation in a Nondissipative Medium.
5.9 Dissipative Medium; Prescribed Distribution in Time.
5.10 Dissipative Medium; Prescribed Distribution in Space.
5.11 Discussion of a Numerical Example.
5.12 Elementary Theory of the Laplace Transformation.
5.13 Application of the Laplace Transformation to Maxwell's Equations.18

DISPERSION.
5.14 Dispersion in Dielectrics.
5.15 Dispersion in Metals.
5.16 Propagation in an Ionized Atmosphere.

VELOCITIES OF PROPAGATION.
5.17 Group Velocity.
5.18 Wave-front and Signal Velocities.

PROBLEMS.

CHAPTER VI: CYLINDRICAL WAVES.

EQUATIONS OF A CYLINDRICAL FIE LD.
6.1 Representation by Hertz Vectors.
6.2 Scalar and Vector Potentials.
6.3 Impedances of Harmonic Cylindrical Fields.

WAVE FUNCTIONS OF THE CIRCULAR CYLINDER.
6.4 Elementary Waves.
6.5 Properties of the Functions Zp(p).
6.6 The Field of Circularly Cylindrical Wave Functions.
6.7 Construction from Plane Wave Solutions.
6.8 Integral Representations of the Functions Zp(p).
6.9 Fourier-Bessel Integrals.
6.10 Representation of a Plane Wave.
6.11 The Addition Theorem for Circularly Cylindrical Waves.

WAVE FUNCTIONS OF THE ELLIPTIC CYLINDER.
6.12 Elementary Waves.
6.13 Integral Representations.
6.14 Expansion of Plane and Circular Waves.

PROBLEMS.

CHAPTER VII: SPHERICAL WAVES.

THE VECTOR WAVE EQUATION.
7.1 A Fundamental Set of Solutions.
7.2 Application to Cylindrical Coordinates.

THE SCALAR WAVE EQUATION IN SPHERICAL COORDINATES.
7.3 Elementary Spherical Waves.
7.4 Properties of the Radial Functions.
7.5 Addition Theorem for the Legendre Polynomials.
7.6 Expansion of Plane Waves.
7.7 Integral Representations.
7.8 A Fourier-Bessel Integral.
7.9 Expansion of a Cylindrical Wave Function.

THE VECTOR WAVE EQUATION IN SPHERICACL COORDINATES.
7.11 Spherical Vector Wave Functions.
7.12 Integral Representations.
7.13 Orthogonality.
7.14 Expansion of a Vector Plane Wave.

PROBLEMS.

THE INHOMOGENEOUS SOLAR WAVE EQUATION.
8.1 Kirchhoff Method of Integration.
8.2 Retarded Potentials.
8.3 Retarded Hertz Vector.

A MULTIPOLE EXPANSION.
8.4 Definition of the Moments.
8.5 Electric Dipole.
8.6 Magnetic Dipole.

RADIATION THEORY OF LINEAR ANTENNA SYSTEMS.
8.7 Radiation Field of a Single Linear Oscillator.
8.8 Radiation Due to Traveling Waves.
8.9 Suppression of Alternate Phases.
8.10 Directional Arrays.
8.11 Exact Calculation of the Field of a Linear Oscillator.
8.12 Radiation Resistance by the E.M.F. Method.

THE KIRCHHOFF-HUYGENS PRINCIPLE.
8.13 Scalar Wave Functions.
8.14 Direct Integration of the Field Equations.
8.15 Discontinuous Surface Distributions.

FOUR-DIMENSIONAL FORMULATION OF THE RADIATION PROBLEM.
8.16 Integration of the Wave Equation.
8.17 Field of a Moving Point Charge.

PROBLEMS.

CHAPTER IX: BOUNDARY-VALUE PROBLEMS.

GENERAL THEOREMS.
9.1 Boundary Conditions.
9.2 Uniqueness of Solution.
9.3 Electrodynamic Similitude.

REFLECTION AND REFRACTION AT A PLANE SURFACE.
9.4 Snell's Laws.
9.5 Fresnel's Equations.
9.6 Dielectric Media.
9.7 Total Reflection.
9.8 Refraction in a Conducting Medium.
9.9 Reflection at a Conducting Surface.

PLANE SHEETS.
9.10 Reflection and Transmission Coefficients.
9.11 Application to Dielectric Media.
9.12 Ahsorbing Layers.

SURFACE WAVES.
9.13 Complex Angles of Incidence
9.14 Skin Effect.

PROPAGATION ALONG A CIRCULAR CYLINDER.
9 15 Natural Modes.
9 16 Conductor Embedded in a Dielectric.
9 17 Further Discussion of the Principal Wave.
9 18 Waves in Hollow Pipes.

COAXIA LINES.
9.19 Propagation Constant.
9.20 Infinite Conductivity.
9.21 Finite Conductivity.

OSCILLATIONS OF A SPHERE.
9.22 Natural Modes.
9.23 Oscillations of a Conducting Sphere.
9.24 Oscillations in a Spherical Cavity.

DIFFRACTION OF A PLANE WAVE BY A SPHERE.
9.25 Expansion of the Diffracted Field.
9.27 Limiting Cases.

EFFECT OF THE EARTH ON THE PROPAGATION OF RADIO WAVES.
9.28 Sommerfeld Solution.
9.29 Weyl Solution.
9.30 van der Pol Solution.
9.31 Approximation of the Integrals.

PROBLEMS.

APPENDIX I.
A. NUMERICAL VALUES OF FUNDAMENTAL CONSTANTS.
B. DIMENSIONS OF ELECTROMAGNETIC QUANTITIES.
C. CONVERSION TABLES.

APPENDIX II.
FORMULAS FROM VECTOR ANALYSIS.

APPENDIX III.
CONDUCTIVITY OF VARIOUS MATERIALS.
SPECIFIC INDUCTIVE CAPACITY OF DIELECTRICS.

APPENDIX IV.
ASSOCIATED LEGENDRE FUNCTIONS.

Index.

Last edited by a moderator: Apr 23, 2017
3. Jan 1, 2008

### nanoWatt

Those books sound excellent. However, I probably would just be lost.

I've decided that I'm going to audit Calculus I in the upcoming semester at a nearby community college. I have a feeling once I get back into the groove I won't really "need" those classes, but a refresher will be great.

I just hope I'm not just punishing myself, since it's going to be college all over again. This time, I don't need the credit.

4. Jan 2, 2008

### mgb_phys

Have a look at the Feynman lectures, a good overview of most physics topics (first 2 vols) and QM (vol 3). It assumes you know the maths so you get more out of them if you already have a physics degree.

5. Jan 2, 2008

### arunma

Hi NanoWatt. I hesitate to make this suggestion, but if you're interested in learning how one arrives at Maxwell's Equations and derives the electromagnetic theory of light, you might try looking at "Classical Electrodynamics" by John D. Jackson. The reason I say that I hesistate to make this suggestion is because it's a graduate level text, and to be quite honest, it's absolutely brutal. I just got done taking graduate E&M, and large portions of my time were spent listening to my fellow students whine about how awful Jackson is, and how Griffiths' undergrad textbook is far more understandable. And they were right; reading Jackson sometimes feels like trying to read Chinese.

Having done my Jackson-bashing, I must admit that it's about as extensive and general as I've found when it comes to the theory of electrodynamics. Except for the insanely complicated integrals that he breezes over, he tends to cover problems in full generality, and explain how we deduce all of these solutions from Maxwell's equations. I wouldn't recommend this as a primary resource, but it's definitely handy to have around if you're interested in the electromagnetic theory of light.

6. Jan 2, 2008

### marcusl

Both Jackson and Stratton are graduate level texts, inappropriate in my mind for someone who might have missed the material the first time around and is struggling with math. Griffiths is a much better choice. You might also look at Schartz, Principles of Electrodynamics, which is an undergrad level book with a Nobelist's sophisticated approach to the unity of electricity and magnetism. (Bonus: it's published by Dover so it's cheap!)

1) Reacquainting yourself with all the vector calculus is essential, and taking a class is an excellent way to do it. Don't think of it as being back in college--you are older, you have a well defined goal that you are pursuing out of passion, and this is a means to achieving it.
3) I believe that things are much easier the second time around. In addition, your motivation and maturity are assets this time around.

7. Jan 2, 2008

### symbolipoint

Taking a course in which you already have credit will probably not be permitted. The school would let you retake a course if you had a low grade and want to have the chance to earn a better one. but if you already have good credit, the school might not allow you to retake. Maybe similar with auditing. You could always just ask to be sure.

8. Jan 2, 2008

### nanoWatt

The community college I will attend for my Calculus classes is one I haven't attended before, because they are closer, and would cost less than a full university. I think all they require is a high school diploma. I will probably take my Physics through UTSA where I graduated. From what I do remember, they allow auditing as long as the pre-reqs are met. If anything, I could take an Independent Study.

9. Jan 3, 2008

### Defennder

Couldn't you just sit in the classes without registering for the course?

10. Jan 3, 2008

### nanoWatt

I want to actually be somewhat involved. I'll probably need to do homework, take the tests, talk with the professor, etc, in order to help me understand. I think auditing in this case would be best.

I actually do have 2 sets of Feynman's lectures, complete with his audio recordings. I don't have vol. 3. I have his Six Easy Pieces and Six not so easy pieces. I'll have to revisit them.

Last edited: Jan 3, 2008
11. Jan 3, 2008

### nanoWatt

I have the Schwartz book in my Amazon cart ready to order. I know things will come back to me, but shouldn't I have a 100% solid understanding of all algebraic factoring, limits, and all the vector calculus before I even begin looking at this book?

I don't want to order calculus books before I see what the class will be using. But I also don't want to have to wait another 2-3 years of just refreshing myself before looking into what I'm interested in.

Also, will this book tell me what would be in Stratton's book? That TOC that was laid out for Stratton looks nice. I don't think at this point I would need both books. There's so much material to go through.

Last edited: Jan 3, 2008
12. Jan 3, 2008

### marcusl

I advise you to order Schwartz or Griffiths or both, start working through it (them) and see how it goes. You'll find out if you need to wait for a math course. As for Feynman, beware that his series isn't effective and effective text for everyone. Threads in the Science Book section show that it works well for only about 50% of students. If it works for you, then you'll learn a lot.

Griffiths is an excellent mainstream E&M text used at top universities everywhere in the country. You wouldn't go wrong there.

I suggested Schwartz as an alternative because it has a different approach that might appeal to you since you say you already covered this material once. Schwartz combines very simple exposition with deep physical insight, and bits of sophistication straight out of a grad level course. Example: In the first chapter he reviews partial derivatives and derives the divergence and curl operators and Gauss's and Stokes's theorems with very physical explanations. Simple too: he writes out the x, y and z components explicitly even though they look similar. In the same chapter he also introduces matrices and tensors of the second rank, which will later be used to demonstrate the relativistic unity of electricity and magnetism. This will definitely stretch you.

These books cover a lot of E&M and will prepare you to go on, but do not come close to covering everything in Stratton. Education is a progression--you take high school physics, then college physics (different subjects in depth), then again but more so in grad school. Each teaches you a lot in its own right, and each also prepares you to move on, but does not substitute for the next level of depth, breadth, and sophistication. I would absolutely steer clear of grad level texts until a) your vector calculus and algebra math skills are solid, b) you feel you've mastered the material in an undergraduate E&M course or book, and c) you've added orthogonal functions (spherical harmonics, Hankel functions, etc.), differential equations (ordinary and partial), and probably tensors to your math repertory. No sense trying Olympic competition before you can swim across the pool with good form and without feeling winded.

Last edited: Jan 3, 2008
13. Jan 3, 2008

### nanoWatt

Thanks for the help. I decided to order the Schwartz, and a book called "How to Solve It" that was recommended on another thread.

I'm finding as I go on that I need less spoon-feeding, but still having steps broken out methodically really helps. I hate when they skip steps assuming the reader knows some "assumed knowledge". But if I plod through slowly to make sure I see where each factor is coming from, that usually helps me. I love to have those aha moments where I finally figure something out.

For me, sometimes it's needing spoon-feeding, sometimes it's me getting in there and trying to understand the relation. I don't quite have my own learning-system figured out yet.

14. Jan 3, 2008

### symbolipoint

From post #9,
Check with the institution that you might like to attend or learn from. You would need to register for the course regardless of what attendance option you use. You could attend for credit + grade, credit or not credit using NO grade, or audit. Usually, priority is given to students attending for a grade, but often enough the class section will have room for a few more students. Check with the institution about the options and registration procedures.

15. Jan 3, 2008

### jesuslovesu

If one were to audit a class, would that person need to attend the labs/do homework and get a "passing" grade? Would the amount of credits that goes towards the class ie 5 count toward the total amount of credits that you would typically take in a semester (18 or so)? I am in a similar position as the OP and wouldn't mind attending a lecture for physics and such, but I don't think I could take 5 credits out of my schedule just for an audit and the lab would be too time consuming as well.

16. Jan 3, 2008

### nanoWatt

AFAIK, auditing doesn't give you a grade or credit. I'm doing the audit because it's cheaper, and I don't need the credit (since I already have a Physics degree). I am mainly concerned with getting myself prepared for graduate work.

I remember once when I was in school, I audited an Optics class because I wasn't quite ready, and wanted the exposure to it. I also worked with the professor in the laser lab. So auditing is good for getting acquainted with the material, but not being concerned with a grade. I will want to know how I'm doing though, so I'm sure there are tests and such.