# Resources for Physics 441

Dr John S. Colton

## Handouts

Here are some handouts I have prepared to help clarify or add information on several selected topics.

- Griffiths-front-and-back-covers.pdf
- Parallel Equations for the Electric and Magnetic Fields.pdf - List of most of the important equations in Phys 441, organized according to electric and magnetic field versions of similar equations
- Physics 441 Formula Sheet.pdf - The parallel equations handout, formatted for 1 page, with other equations potentially needed for exams added to the end.
**This is the one you should print out, handwrite anything else you'd like on it, and bring to the Testing Center for the exams.** - What you should already know about electric field and potential.pdf (approx lecture 1)
- field from a spherical shell.nb - Mathematica code demonstrating the "Assuming" command (approx lecture 6)
- legendre polynomials.pdf - summary of information about the Legendre polynomials (approx lecture 13)
- relaxation examples.pdf - output images for some relaxation examples shown in class (approx lecture 13)
- field lines of a pure electric dipole.nb - Mathematica notebook to plot the field lines of a pure electric dipole, namely
**E**= C/r^{3}(2 cos(theta)**r-hat**+ sin(theta)**theta-hat**). I may or may not discuss this in class; if not I likely at least talked about how that combination of 2 cos(theta)**r-hat**+ sin(theta)**theta-hat**is special (approx lecture 14) - Quadrupole Moment and Potential.pdf (approx lecture 15)
- charge density from image problem.nb - Mathematica notebooks for the canonical image problem (approx lecture 17)
- orthogonality of sine functions.nb - Mathematica notebook demonstrating the orthogonality of sine functions (approx lecture 18)
- separation of variables - 2D semi-infinite.nb - Mathematica notebook for separation of variables 2D semi-infinite problem (approx lecture 18)
- separation of variables - 3D cube.nb - Mathematica notebook for separation of variables 3D cube problem (approx lecture 19)
- worked SOV problem given sigma on a shell.pdf - worked separation of variables problem likely discussed very quickly in class (approx lecture 20)
- Electric fields around spheres.pdf - figures from Griffiths of electric fields around spheres (approx lecture 21)
- griffiths-figs-3.37b-and-5.55b.pdf - figures from Griffiths of fields from electric and magnetic dipoles (approx lecture 30)
- field of magnetized cylinder - z axis.pdf | field of magnetized cylinder - z axis.nb - Mathematica notebook to plot the magnetic field from a magnetized cylinder (approx lecture 33)
- Gaussian units.pdf - handout for lecture on Gaussian units (not in Griffiths) (approx lecture 39)

## Past Exams

On the exams, I will give you the front and back inside covers of Griffiths, along with a limited selection of integrals which will include any ones you need which are more complicated that polynomials, exponentials, sines and cosines, and that typeo of thing. Here's the start of Exam 1 from Spring 2021

Here are a few actual exams from past semesters. If you are using these to study, I highly recommend you work out the exams on your own BEFORE looking at the solutions. Also note that the coverage from year to year is not necessarily consistent, both in terms of overall material covered and material covered for each exam. For that matter, some semester we've had two midterm exams and other semesters three midterms.

- Exam 1
- Exam 1 - Spring 2016.docx | Exam 1 - Spring 2016 - solutions.pdf
- Caught an error in the solutions--multiple choice problem 1.6 should say that
**B1**will be in the z-direction, not the y-direction.

- Caught an error in the solutions--multiple choice problem 1.6 should say that
- Exam 1 - Fall 2016.docx | Exam 1 - Fall 2016 - solutions.pdf
- Exam 1 - Fall 2017.docx | Exam 1 - Fall 2017 - solutions.pdf
- Exam 1 - Fall 2018.docx | Exam 1 - Fall 2018 - solutions.pdf

- Exam 1 - Spring 2016.docx | Exam 1 - Spring 2016 - solutions.pdf
- Exam 2
- Exam 2 - Spring 2016.docx | Exam 2 - Spring 2016 - solutions.pdf
- Exam 2 - Fall 2016.docx | Exam 2 - Fall 2016 - solutions.pdf- Oops, looks like there are a couple of errors in the solutions:
- Problem 1.9 (multiple choice) - my logic is good, but I accidentally wrote // instead of perpendicular in my description of the second boundary condition.
- I dropped a negative sign from the bound volume charge density of problem 5.

- Exam 2 - Fall 2017.docx | Exam 2 - Fall 2017 - solutions.pdf
- Exam 2 - Fall 2018.docx | Exam 2 - Fall 2018 - solutions.pdf

- Exam 3 - See note above about the difference in material from previous semesters
- Exam 3 - Spring 2016.docx | Exam 3 - Spring 2016 - solutions.pdf
- Oops, it looks like in problem 5 I may have calculated the field for points with z<a. If z is between a and b, then the area in the calculation of the enclosed free current should be (2a lprime) instead of (2z lprime). That'll affect the answers after that point.

- Exam 3 - Fall 2016.docx | Exam 3 - Fall 2016 - solutions.pdf
- Exam 3 - Fall 2017.docx | Exam 3 - Fall 2017 - solutions.pdf
- Exam 3 - Fall 2018.docx | Exam 3 - Fall 2018 - solutions.pdf

- Exam 3 - Spring 2016.docx | Exam 3 - Spring 2016 - solutions.pdf
- Final Exam
- Final Exam - Spring 2016.docx | Final Exam - Spring 2016 - solutions.pdf - Oops, in the solution for problem 2a the denominator of the second term should be sqrt((d-a/2)^2 + (a/2)^2) instead of sqrt((d+a/2)^2 - (a/2)^2).
- Final Exam - Fall 2016.docx | Final Exam - Fall 2016 - solutions.pdf (with last page removed, since it was used as a homework problem in a later semester)
- Final Exam - Fall 2017.docx | Final Exam - Fall 2017 - solutions.pdf
- Final Exam - Fall 2018.docx | Final Exam - Fall 2018 - solutions.pdf