PHYSICS

1. PHYSICS adapted from http://www.nearingzero.net (nz128)

2. Today’s agenda: Announcements. Warning: excessive announcements can cause stress and high blood pressure. Gauss’ Law Examples. You must be able to use Gauss’ Law to calculate the electric field of a high-symmetry charge distribution. Cultural enlightenment time. You must be culturally enlightened by this lecture. Conductors in electrostatic equilibrium. You must be able to use Gauss’ law to draw conclusions about the behavior of charged particles on, and electric fields in, conductors in electrostatic equilibrium.

3. Announcements  Exam 1 is Tuesday, February 18, 5:00-6:15 pm. If you are participating in an official Missouri S&T event or in a class that offers no makeups, a sponsor may administer the test and provide test security. See “Taking a Test at a Different Time/Place” on this web page. I will need a brief memo from you (handwritten is OK), signed by you and your faculty sponsor or course instructor, no later than end of the 1:00 lecture on the Wednesday before the exam (Feb. 12 for Exam 1). Instead of a signed memo, E-mails (they could be separate) from both you and your sponsor/instructor are also sufficient. I just need to know that your sponsor is fully informed.

4. Announcements (continued)  Exam 1 is Tuesday, February 18, 5:00-6:15 pm. In case of a officially-scheduled course conflict, there is an option to take the test from 5:30-6:45 on Test Day. In case you have a later conflict, this semester I will also provide option to take the test from 4:30-5:45 on Test Day. You will not be allowed to leave the exam room before 5:30 pm. If one of the above two circumstances applies to you, send me an e-mail by no later than end of the 1:00 lecture on the Wednesday before the exam (Feb. 12 for Exam 1), telling me when you will need to take the exam (either 4:30 or 5:30). Also provide the reason* for the conflict (e.g. “CS 54 Lab”). *You were supposed to not schedule a class that conflicts with exams!

5. Announcements (continued) E-mail me right away if you have a time conflict for Exam 1 which is not covered on the previous two slides slide. Provide these details: (1) dates of conflict, (2) nature of conflict, (3) name of “responsible” person (other course instructor, job supervisor, etc.). There are no guarantees, but perhaps the other person involved and I will work out something agreeable.

6. Announcements (continued)  The Missouri S&T Testing Centerprovides accommodations for students with special needs or disabilities. According to Testing Center guidelines: both students and faculty must separately make appointments. I must submit my requests seven days prior to the test. Same-day requests are not accepted. To ensure that we meet these guidelines, I need to be informed no later than Friday, February 7, that you will require Testing Center accommodations for Exam 1. I will then request the necessary accommodations. Also provide me with your accommodation letter and Missouri S&T e-mail address by the end of the 1:00 Wednesday lecture prior to the test (February 12 for Exam 1).

7. Announcements (continued) If you are going to miss recitation due to illness or other special circumstances, let your recitation instructor know. That will not necessarily excuse you from boardwork and will not excuse you from turning in homework. Find a way to get your homework to your recitation instructor before the start of recitation. Have a friend take it. Scan and e-mail it. Photograph and e-mail it (keep file sizes down!). Take a picture with your cell phone camera and e-mail it. (Clear this with your recitation instructor so he/she knows you didn’t take a photo of someone else’s work.) This does not constitute blanket permission to turn in homework electronically or to skip recitation. You are expected to attend recitation, and bring homework on paper. Always get clearance from your recitation instructor for special circumstances!

8. Announcements (continued) I am not your recitation instructor! Do not put my name in the “recitation instructor” box of your lab reports. If you do so, there is no guarantee your recitation instructor will get the lab report (which he/she uses to record lab grades). Your recitation instructor should be your first contact person for dealing with problems with Physics 24. If you do email me about a problem, please include your recitation section letter in the email. Know your recitation section letter!

9. Announcements (continued) Walk-in tutors in 208 Norwood are available from 7-9 pm Monday through Thursday.  One of the homework problems for tomorrow is Special Homework #3. You can find it on the web here.

10. This Lecture…

11. Gauss’ Law Last time we learned that Gauss’ Law Always true, not always easy to apply. Today we will calculate electric fields for charge distributions that exhibit a high degree of symmetry… …and we will save more complex charge distributions for advanced classes.

12. Today’s agenda: Announcements. Gauss’ Law Examples. You must be able to use Gauss’ Law to calculate the electric field of a high-symmetry charge distribution. Cultural enlightenment time. You must be culturally enlightened by this lecture. Conductors in electrostatic equilibrium. You must be able to use Gauss’ law to draw conclusions about the behavior of charged particles on, and electric fields in, conductors in electrostatic equilibrium.

13. Example: calculate the electric field outside a long cylinder of finite radius R with a uniform volume charge density  spread throughout the volume of the cylinder. I didn’t finish this during lecture 3, so will do it today. See the lecture 3 notes for hints. More details of the calculation shown here: http://campus.mst.edu/physics/courses/24/Handouts/charged_cylinder.pdf

14. Example: use Gauss’ Law to calculate the electric field due to a long line of charge, with linear charge density . Example: use Gauss’ Law to calculate the electric field due to an infinite sheet of charge, with surface charge density . These are easy using Gauss’ Law (remember what a pain they were in the previous chapter). Study these examples and others in your text! There will be more examples of applications of Gauss’ law near the end of this lecture.

15.  Solve for E. Strategy for Solving Gauss’ Law Problems  Select a Gaussian surface with symmetry that “matches” the charge distribution. Use symmetry to determine the direction of on the Gaussian surface. You want to be constant in magnitude and everywhere perpendicular to the surface, so that … … or else everywhere parallel to the surface so that .  Evaluate the surface integral (electric flux).  Determine the charge inside the Gaussian surface.

16. Gauss’ Law works well for three kinds of symmetry: Charge SymmetryGaussian Surface spherical concentric sphere cylindrical coaxial cylinder planar pillbox

17. “Quiz” time (maybe for points, maybe just for practice!)

18. Today’s agenda: Announcements. Gauss’ Law Examples. You must be able to use Gauss’ Law to calculate the electric field of a high-symmetry charge distribution. Cultural enlightenment time. You must be culturally enlightened by this lecture. Conductors in electrostatic equilibrium. You must be able to use Gauss’ law to draw conclusions about the behavior of charged particles on, and electric fields in, conductors in electrostatic equilibrium.

19. Cultural Enlightenment* Time The top 5 reasons why we make you learn Gauss’ Law: 5. You can solve difficult (high-symmetry) problems with it. 4. It’s good for you. It’s fun! What more can you ask! 3. It’s easy. Smart physicists go for the easy solutions. 2. If I had to learn it, you do too. And the number one reason… …will take a couple of slides to present *This will not be tested on the exam.

20. You have learned the integral form of Gauss’ Law: This equation can also be written in differential form: a 3-dimensional derivative operator Now you can see we are on the trail of something Really Big… This will not be tested on the exam.

21. The Missouri S&T Society of Physics Students T-Shirt! This will not be tested on the exam.

22. Today’s agenda: Announcements. Gauss’ Law Examples. You must be able to use Gauss’ Law to calculate the electric field of a high-symmetry charge distribution. Cultural enlightenment time. You must be culturally enlightened by this lecture. Conductors in electrostatic equilibrium. You must be able to use Gauss’ law to draw conclusions about the behavior of charged particles on, and electric fields in, conductors in electrostatic equilibrium.

23. Conductors in Electrostatic Equilibrium Homework hints buried in the next 3 slides! Electrostatic equilibrium means there is no net motion of tne charges inside the conductor. The electric field inside the conductor must be zero. If this were not the case, charges would accelerate. Any excess charge must reside on the outside surface of the conductor. Apply Gauss’ law to a Gaussian surface just inside the conductor surface. The electric field is zero, so the net charge inside the Gaussian surface is zero. Any excess charge must go outside the Gaussian surface, and on the conductor surface.

24. The electric field just outside a charged conductor must be perpendicular to the conductor’s surface. Otherwise, the component of the electric field parallel to the surface would cause charges to accelerate. The magnitude of the electric field just outside a charged conductor is equal to /0, where  is the magnitude of the local surface charge density. A simple application Gauss’ Law, which I will show if time permits.

25. If there is an empty nonconducting cavity inside the conductor, Gauss’ Law tells us there is no net charge on the interior surface of the conductor. Construct a Gaussian surface that includes the inner surface of the conductor. The electric field at the Gaussian surface is zero, so no electric flux passes through the Gaussian surface. Gauss’ Law says the charge inside must be zero. The conductor does not have to be symmetric, as shown. If there is a nonconducting cavity inside the conductor, with a net charge inside the cavity, Gauss’ Law tells us there is an equal and opposite induced charge on the interior surface of the conductor. Construct a Gaussian surface that includes the inner surface of the conductor. The electric field at the Gaussian surface is zero, so no electric flux passes through the Gaussian surface. Gauss’ Law says the charge inside must be zero. Construct a Gaussian surface that includes the inner surface of the conductor. The electric field at the Gaussian surface is zero, so no electric flux passes through the Gaussian surface. Gauss’ Law says the charge inside must be zero. There must be a –Q on the inner surface. The conductor does not have to be symmetric, as shown. +Q -Q

26. Example: a conducting spherical shell of inner radius a and outer radius b with a net charge -Q is centered on point charge +2Q. Use Gauss’s law to show that there is a net charge of -2Q on the inner surface of the shell, and a net charge of +Q on the outer surface of the shell. -Q a +2Q b Thanks to Dr. Waddill for the use of the picture.

27. r Example (if time permits): an insulating sphere of radius a has a uniform charge density ρ and a total positive charge Q. Calculate the electric field at a point inside the sphere a Q Thanks again to Dr. Waddill for the use of the picture.

28. Because there may not be time to work the previous two examples in class, I will put Dr. Waddill’s lecture on Gauss’ Law from a couple of years ago on the Physics 24 web site. Please click on the word “lecture” in the previous sentence to view/download the lecture. Here is the address for you to copy and paste into a web browser, in case the link in the above paragraph doesn’t work: http://campus.mst.edu/physics/courses/24/Handouts/Lec_03.ppt

29. Demo: Professor Tries to Avoid Debilitating Electrical Shock While Demonstrating Van de Graaff Generator http://en.wikipedia.org/wiki/Van_de_Graaff_generator