PHYS 211 Final, Fall 2008

PHYSICS 211 Final EXAM FALL 2008-09 TIME: 120 minutes January 27, 2009 DO NOT OPEN THIS EXAM BEFORE YOU ARE TOLD TO BEGIN NAME________________________________________________ ID Number ________________________ Useful information 0=8.85x10-12 C2/N.m2. 0=4p x 10-7 Tm/A. q = 1.6  1019 C me= 9.1x10-31 kg. mp= 1.67×10-27 kg. ke=8.9875x109 Nm2/C2 The solution for the differential equation of the form dy/dt + ay = b is y=(b/a)(1-exp(-at)) Grading A B TOTAL Score:________ Check if solution is continued on the back. 1 Part A: Multiple choice questions (20) each question has 2 points 1. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = –80 nC, and q = 36 nC in the figure, what is the magnitude of the total electric force on q? a. 5.0 N b. 4.4 N c. 3.8 N d. 5.7 N e. 0.60 N 2. A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown. Where is the induced charge density greatest in magnitude and what is its sign? a. A; negative. b. A; positive. c. B; negative. d. B; positive. e. C; negative. 3. The electric potential inside a charged solid spherical conductor in equilibrium a. is always zero. b. is constant and equal to its value at the surface. c. decreases from its value at the surface to a value of zero at the center. d. increases from its value at the surface to a value at the center that is a multiple of the potential at the surface. e. is equal to the charge passing through the surface per unit time divided by the resistance. Score:________ Check if solution is continued on the back. 2 4. 5. To increase the current density in a wire of length 􀁁 and diameter D, you can a. decrease the potential difference between the two ends of the wire. b. increase the potential difference between the two ends of the wire. c. decrease the magnitude of the electric field in the wire. d. heat the wire to a higher temperature. e. combine both (b) and (d). 6. When a capacitor is fully charged, the current through the capacitor is a. zero. b. at its maximum value. c. equal to the current in a resistive circuit in parallel with the capacitor circuit. d. greater than the current in a resistor that is farther from the battery than the capacitor. e. zero if it is the only capacitor, but maximum if there is another capacitor in series with it. 7. A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I travels in the direction shown in the magnetic field B. Score:________ Check if solution is continued on the back. 3 a. 2IBL in the –z direction b. 2IBL in the +z direction c. 4IBL in the +z direction d. 4IBL in the –z direction e. zero 8. 9. An induced emf is produced in a. a closed loop of wire when it remains at rest in a nonuniform static magnetic field. b. a closed loop of wire when it remains at rest in a uniform static magnetic field. c. a closed loop of wire moving at constant velocity in a nonuniform static magnetic field. d. all of the above. e. only b and c above. 10. Part B- Problems (80 %) Score:________ Check if solution is continued on the back. 4 1.(30) In order to determine the effect of a resistance, capacitance and inductance on an AC circuit, we put each of them independently in series with a voltage source v=Vmax sin(2ft). (This problem is analytical). a(5) Use the three circuits above to calculate the analytical expression of the current in each of the circuits. b(5) Use the expressions found to determine the impedance of each of the circuits and the phase shift of the current in each circuit with respect to v. State also the units of the different impedance. Score:________ Check if solution is continued on the back. 5 c(5) Determine the analytical formula of the instantaneous power dissipated in each of the circuits. d(6) Demonstrate that the power integrated over one cycle is equal to zero when the capacitor and the inductor are put in series with the power supply v=Vmax sin(2ft). Score:________ Check if solution is continued on the back. 6 e(4) Determine the analytical expression of the average power dissipated as a function of the three impedance (R, XL and Xc) f(5) Calculate the frequency at which maximum power is dissipated. Score:________ Check if solution is continued on the back. 7 2.(25) The switch in Figure below is open for t < 0 and then closed at time t = 0. (a)(15) Use Kirchhoffs’ rules to find the current in the three resistors as a function of time just after closing the switch. Score:________ Check if solution is continued on the back. 8 (b)(10) The switch is opened, find the time dependence of three currents in the three resistors just after. Score:________ Check if solution is continued on the back. 9 3.(25%) A conducting rod of length ℓ = 35.0 cm is free to slide on two parallel conducting bars as shown in the figure below. Two resistors R1 = 2.00 Ω and R2 = 5.00 Ω are connected across the ends of the bars to form a loop. A constant magnetic field B = 2.50 T is directed perpendicularly into the page. An external agent pulls the rod to the left with a constant speed of v = 8.00 m/s. Score:________ Check if solution is continued on the back. 10 (a) (5)Determine the current directions on the two resistors. (b) (10) Find the currents amplitude in both resistors Score:________ Check if solution is continued on the back. 11 (c) (5)Find the total power delivered to the resistance of the circuit (d) (5)Find the magnitude of the applied force that is needed to move the rod with this constant velocity. Score:________ Check if solution is continued on the back. 12 SCRATCH PAPER Nothing on this page will be graded Score:________ Check if solution is continued on the back. 13 Score:________ Check if solution is continued on the back. 14