Phy207 Exam II (Form1) Professor Zuo Fall Semester 2015 On my honor, I have neither received nor given aid on this examination Signature: Name: #1 14 #15 ID number: Total Enter your name and Form 1 (FM1) in the scantron sheet. Attempt all problems. Multiple choice questions 1-14 are worth 5pts each and the essay problem 15 is worth 30 pts plus 5 extra credits for part D. This is a closed book exam, you must work independently! No collaboration is allowed. Prohibited items: any electronic devices including cell phones and calculators, pens, backpacks, notes, books. Anyone found cheating during the exam will automatically receive an F grade for the course and sent to the honor s court. Put an X next to your discussion section: [ ] Dr. Mezincescu 5P, 11:00 11:50 a.m. [ ] Dr. Zuo 5Q, 12:30 1:20 p.m. [ ] Dr. Zuo 5R, 2:00 2:50 p.m. [ ] Dr. Barnes 5S, 3:30 4:20 p.m. [ ] Dr. Barnes 5T, 5:00 5:50 p.m.
1. Points R and T are each a distance d from each of two particles with charges of equal magnitudes and opposite signs as shown. If k = 1/40, the work required to move a particle with negative charge q from R to T is: A) 0 B) kqq/d 2 C) kqq/d D) / 2 E) kqq/(2d) 2. Two conducting spheres are far apart. The smaller sphere carries a total charge of Q. The larger sphere has a radius that is twice that of the smaller and is neutral. After the two spheres are connected by a conducting wire, the charges on the smaller and larger spheres, respectively, are: A) Q/2 and Q/2 B) Q/3 and 2Q/3 C) 2Q/3 and Q/3 D) 0 and Q E) 2Q and Q 3. The electric potential around a certain point is given by V = 7.5x 2 + 3x, where V is in volts and x is in meters. What is the electric field at that point? A) = (15x 3) B) = ( 15x + 3) C) = ( 2.5x 3 + 1.5 x 2 ) D) = (2.5x 3 1.5 x 2 ) E) = 0 4. A capacitor is filled with dielectric materials as shown in the figure. The and materials have equal height d/2 each, and have the same width as the material. What is the total capacitance of the capacitor if, 2 and 3 A) B) C) D) E)
5. All capacitors have the same capacitance C and all batteries have the same emf, as shown in the diagram. Find the electric field energy contained by the capacitor marked C in the figure (hint: choose an appropriate loop). A) B) C) D) 2 E) 0 6. A cylindrical copper rod has resistance R. It is stretched to twice its original length with no change of volume. Its new resistance is: A) R/2 B) R C) 2R D) 4R E) 8R For the next three problems, consider a multiloop circuit shown in the figure. It is not necessary to solve the entire circuit. 7. Compared to the polarity shown in the figure, the emf ε1 is closest to A) -5 V, B) 5 V, C) 45 V, D) 51 V, E) -51 V. 8. What is current I1? A) 5A, B) 2A, C) A, D) A, E) none of above 9. What is current I2? A) 5A, B) 7A, C) 3A, D) 0A, E) -3A
For the next five questions consider two concentric spherical conducting shells with inner radius a and outer radius b for the inner shell and inner radius c and outer radius d for the outer shell are charged with q and q, respectively. 10. Find the electric field in the region between the two shells b<r<c. A) B) C) D) E) 0 11. Find the potential difference between the two conductors. A) B) C) D) E) 12. Assuming potential is zero at infinite, find the electric potential at the center of the shells. A) V=0 B) V= C) V= D) E)
13. Find the electric field energy du contained within a thin spherical shell of radius r (b<r<c) and thickness dr in terms of electric field E(r). A) B) 2 C) 4 D) 4 E) 14. Find the radius R where the electric field energy stored within it (rr) is half of the total energy. A) R= B) C) D) E)
15. In the circuit shown below the switch has been left open for a long time. At t=0, the switch S is closed. To simplify the calculation, take R1=R2=R, R3=2R and express your answers in terms of, R and C. A) Find the current going through the capacitor immediately after S is closed. B) Find the energy Uo stored by the capacitor long after S is closed. C) After S has been closed for a long time, the switch S is opened again (reset the clock to t=0 again), how long after that will the energy remaining in the capacitor be equal to Uo/e (express the time in terms of quantities given in the problem)? D) (extra credit question 5pts) Find the time constant of the circuit after S is closed as in part A) and B). A) Immediately after S is closed, the charge on the capacitor remains temporarily zero, thus zero potential drop cross the capacitor. The current going through the capacitor branch can be calculated simply in terms of finding the total current and the splitting between R2 and R3. The total equivalent resistance of the three is 5/3R, and the total current going through R1 is then, splitting at the junction will lead to. B) After a long time, the current going through the C branch is zero, resulting a steady current of. The voltage drop across the capacitor is the same as the voltage across R2, i.e. The energy stored is then given by. C) After S is opened again, the charged capacitor discharges through R2 and R3 (in series). The charge remaining on the capacitor. The energy on the capacitor is given by. At, the energy remaining is reduced to Uo/e. D) Rather than setting up the differential equation that relates the time dependence of the current going through the capacitor and the charge on it. An easier way to solve the problem is to understand that the time constant is the same for either charging or discharging process if the circuit remains the same. The time constant for the discharging is very easy to calculate, the equivalent resistance is 2R+1/2R=(5/2)R, thus the time constant is.