Physics 24 Exam

1. That reminds me… must pick up test prep HW. Physics 24 Exam adapted from http://www.nearingzero.net (nz118.jpg)

2. Announcements  Grades spreadsheets will be posted the day after Exam 1. You will need your PIN to find your grade. If you haven’t received your PIN yet, it will be on your exam or it will be emailed to you.* If you lose your PIN, ask (politely and apologetically) your recitation instructor. If you haven’t received it yet, ask your instructor about it tomorrow in recitation. *No PIN = you can’t look up your exam grade ahead of time! Have to go to recitation.

3. Physics 24 Test Room Assignments, Spring 2014: Instructor Sections Room Dr. Hale F, H G-31 EECH Dr. Parris G, L 125 BCH Mr. Upshaw E, K 199 Toomey Mr. Viets A, C 104 Physics Dr. Vojta B, D G-3 Schrenk 4:30 & 5:30 Exams 202 Physics Special Needs Testing Center Exam is from 5:00-6:15 pm! Know the exam time! Find your room ahead of time! If at 5:00 on test day you are lost, go to 104 Physics and check the exam room schedule, then go to the appropriate room and take the exam there.

4. Reminders: No external communication allowed while you are in the exam room. No texting! No cell phones! Please do not leave the exam room before 5:30 pm. Be sure to bring a calculator! You will need it. No headphones.

5. Do you know the abbreviations for: milli- micro- nano- pico-? Will you know them by 5:00 pm tomorrow?

6. Exam 1 Review The fine print: the problems in this lecture are the standard “exam review lecture” problems and are not a guarantee of the exam content. Please Look at Prior Tests! Caution: spring 2011 exam 1 did not cover capacitors—not true this semester.

7. Overview Electric charge and electric force Coulomb’s Law Electric field calculating electric field motion of a charged particle in an electric field Gauss’ Law electric flux calculating electric field using Gaussian surfaces properties of conductors Exam problems may come from topics not covered on test preparation homework or during the review lecture.

8. Overview Electric potential and electric potential energy calculating potentials and potential energy calculating fields from potentials equipotentials potentials and fields near conductors Capacitors capacitance of parallel plates, concentric cylinders, (concentric spheres not for this exam) equivalent capacitance of capacitor network Don’t forget concepts from physics 23 that we used! Exam problems may come from topics not covered on test preparation homework or during the review lecture.

9. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total negative charge -Q uniformly distributed over its length. What is the electric field at the origin? y x a

10. What would you do differently if we placed a second eighth of a circle in the fourth quadrant, as shown? y x a

11. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total negative charge -Q uniformly distributed over its length. A negative point charge -q is placed at the origin. What is the electric force on the point charge? Express your answer in unit vector notation. y x a

12. An insulating spherical shell has an inner radius b and outer radius c. The shell has a uniformly distributed total charge +Q. Concentric with the shell is a solid conducting sphere of total charge +2Q and radius a<b. Find the magnitude of the electric field for r<a. This looks like a test preparation homework problem, but it is different!

13. An insulating spherical shell has an inner radius b and outer radius c. The shell has a uniformly distributed total charge +Q. Concentric with the shell is a solid conducting sphere of total charge +2Q and radius a<b. Use Gauss’ Law to find the magnitude of the electric field for a<r<b. This looks like a test preparation homework problem, but it is different! Be able to do this: begin with a statement of Gauss’s Law. Draw an appropriate Gaussian surface on the diagram and label its radius r. Justify the steps leading to your answer.

14. An insulating spherical shell has an inner radius b and outer radius c. The shell has a uniformly distributed total charge +Q. Concentric with the shell is a solid conducting sphere of total charge +2Q and radius a<b. Find the magnitude of the electric field for b<r<c. What would be different if we had concentric cylinders instead of concentric spheres? What would be different if the outer shell were a conductor instead of an insulator?

15. An electron has a speed v. Calculate the magnitude and direction of a uniform electric field that will stop this electron in a distance D. Know where this comes from! Do you understand that these E’s have different meanings? Use magnitudes if you have determined direction of E by other means.

16. You can also use kinematics to solve this problem. Why? Possible variations on the previous problem (the “same” problem, but students would disagree)… …calculate the closest the electron would come to another electron...or… …calculate the minimum initial speed an electron needs to escape from a proton a distance D away.

17. Two equal positive charges Q are located at the base of an equilateral triangle with sides of length a. What is the potential at point P (see diagram)? P a Q Q

18. An electron is released from rest at point P. What path will the electron follow? What will its speed be when it passes closest to either charge Q? P a Q Q

19. Three equal positive charges Q are located at the corners of an equilateral triangle with sides of length a. What is the potential energy of the charge located at point P (see diagram)? P Q a Q Q What would happen if the charges were held at rest in the above configuration, and then released?

20. If you need to evaluate an integral on tomorrow’s exam, you will be given the integral. Exception: xn where n is a real number. If you don’t know what you are doing, pretend that you do and write stuff down. You might know more than you think you do!

21. C1 C2 C3 V0 For the capacitor system shown, C1=6.0 F, C2=2.0 F, and C3=10.0 F. (a) Find the equivalent capacitance. Don’t expect the equivalent capacitance to always be an integer!

22. C1 C2 C3 V0 For the capacitor system shown, C1=6.0 F, C2=2.0 F, and C3=10.0 F. (b) The charge on capacitor C3 is found to be 30.0 C. Find V0.

23. Summary of all the “things you must be able to do” slides. Lecture 1: Coulomb’s Law (electrical force between charged particles). You must be able to calculate the electrical forces between two or more charged particles. Lecture 2: The electric field. You must be able to calculate the force on a charged particle in an electric field. Electric field of due to a point charge. You must be able to calculate electric field of a point charge. Motion of a charged particle in a uniform electric field. You must be able to solve for the trajectory of a charged particle in a uniform electric field. The electric field due to a collection of point charges. You must be able to calculate electric field of a collection of point charges. The electric field due to a continuous line of charge. You must be able to calculate electric field of a continuous line of charge.

24. Lecture 3: The electric field of a dipole. You must be able to calculate the electric field of a dipole. The electric field due to a collection of point charges (continued). You must be able to calculate the electric field of a collection of point charges. Electric field lines. You must be able to draw electric field lines, and interpret diagrams that show electric field lines. A dipole in an external electric field. You must be able to calculate the moment of an electric dipole, the torque on a dipole in an external electric field, and the energy of a dipole in an external electric field. Lecture 4: Electric flux. You must be able to calculate the electric flux through a surface. Gauss’ Law. You must be able to use Gauss’ Law to calculate the electric field of a high-symmetry charge distribution. 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.

25. Lecture 5: Electric potential energy. You must be able to use electric potential energy in work-energy calculations. Electric potential. You must be able to calculate the electric potential for a point charge, and use the electric potential in work-energy calculations. Electric potential and electric potential energy of a system of charges. You must be able to calculate both electric potential and electric potential energy for a system of charged particles (point charges today, charge distributions next lecture). The electron volt. You must be able to use the electron volt as an alternative unit of energy.

26. Lecture 6: Electric potential of a charge distribution. You must be able to calculate the electric potential for a charge distribution. Equipotentials. You must be able to sketch and interpret equipotential plots. Potential gradient. You must be able to calculate the electric field if you are given the electric potential. Potentials and fields near conductors. You must be able to use what you have learned about electric fields, Gauss’ law, and electric potential to understand and apply several useful facts about conductors in electrostatic equilibrium. Lecture 7: Capacitance. You must be able to apply the equation C=Q/V. Capacitors: parallel plate, cylindrical, spherical. You must be able to calculate the capacitance of capacitors having these geometries, and you must be able to use the equation C=Q/V to calculate parameters of capacitors. Circuits containing capacitors in series and parallel. You must be understand the differences between, and be able to calculate the “equivalent capacitance” of, capacitors connected in series and parallel.