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# Test2 - zzIyer Savi V Physics 125 Analytical Physics II...

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Unformatted text preview: zzIyer, Savi V Physics 125, Analytical Physics II Date Thr, Mar 13, 2008 at 21:00 Section 99 Exam 2 4. [6pt] The figure shows the equipotential contours due to three point charges. The labels on the contours are in Volts. Indicate T-True or F-False for each statement. 1. [6pt] Consider the infinite sheet of charge shown. It has a surface charge density of (units C/m2 ). A cylindrical Gaussian Surface is also shown. Indicate T-True or F-False for each statement. + + + + + + + + P Q A) The Field at Q is /20 B) If this were a negatively charged sheet, the area vector at Q would point towards the sheet. C) The type of symmetry exploited here is cylindrical symmetry D) E dA for the surface near Q is zero. E) It would have made the calculation of the E-Field significantly more difficult if we had used a Gaussian Surface with a rectangular cross-section rather than a circular cross-section. F) E dA for the surface near P is zero. 2. [4pt] A dielectric plate is inserted between the plates of the lower of the two identical capacitors in the figure. Which one of the following statements is true? A) A charge released from rest on one of these contours will move along the contour. B) 118.1 J of work is done to move a charge of 1 Coulomb from c to d along the contour. C) Two of the charges are positive and one is negative. D) The charge located at (0,0) is greater than the charge located at (-5,5). E) The electric field at e is directed normal to the 221.7 V contour and away from the 312.1 V contour. F) The potential at b is greater than at a. 5. [6pt] Consider a very large nonconducting slab with thickness d = 3.9 mm and uniform volume charge density = 3.7 nC/m3. What is the magnitude of the electric field 1/5 of the way into the slab (that is, a distance 0.780 mm from one of the surfaces), in units N/C? A) 4.89 10-1 E) 1.19 B) 6.11 10-1 F) 1.49 C) 7.64 10-1 G) 1.87 D) 9.55 10-1 H) 2.33 A) The potential energy stored in the upper capacitor decreases. B) The charge on the lower capacitor remains the same. C) The capacitance of the lower capacitor decreases. D) The potential difference across the lower capacitor decreases. E) The charge on the upper capacitor decreases. 6. [4pt] Three charges are at rest on the xy-plane: q1 = 1.35 C at (4.00 m, 0), q2 = 7.60 C at (0, 2.75 m), and q3 = -4.50 C at (4.00 m, 2.75 m). What is the electric potential (in V) at the origin? 4 4 4 4 A) 1.95 10 B) 2.21 10 C) 2.50 10 D) 2.82 10 3. [4pt] Two point charges, A and B, lie along a line sepaE) 3.19 104 F) 3.60 104 G) 4.07 104 H) 4.60 104 rated by a distance L. The point "x" is at the midpoint of their separation. 7. [6pt] A fourth charge q4 = 2.35 C is brought and placed at the origin. Calculate the total potential energy (in mJ) of this system of four charges. A B Which combination of charges will yield zero electric potential at point "x"? A) -1q and +4q B) +2q and -3q C) +1q and -4q D) +4q and +4q E) +1q and -1q A) -2.32 101 E) -4.35 101 B) -2.72 101 F) -5.09 101 C) -3.18 101 G) -5.96 101 D) -3.72 101 H) -6.97 101 (Please turn to the next page...) zzIyer, Savi V Physics 125, Analytical Physics II Section 99 Exam 2 13. [5pt] Two capacitors C1 = 6.6 F, C2 = 15.7 F are charged individually to V1 = 13.8 V, V2 = 4.6 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together. Calculate the final potential difference (in V) across the plates of the capacitors once they are connected. A) 5.51 E) 1.72 101 B) 7.32 F) 2.29 101 C) 9.74 G) 3.05 101 D) 1.30 101 H) 4.05 101 8. [6pt] An electron is initially a great distance from a proton with an initial speed of 7.20 105 m/s. It is aimed so that it passes near the proton, which is essentially fixed in place. At the distance of nearest approach, the electron's instantaneous speed is found to be 1.37 106 m/s. What was the distance of nearest approach to the proton (in nm)? electron proton 14. [5pt] By how much is the total stored energy reduced when the two capacitors are connected, in units of J? D) 1.92 10-1 H) 4.68 10-1 A) 1.07 10-4 E) 1.74 10-4 B) 1.21 10-4 F) 1.97 10-4 C) 1.36 10-4 G) 2.22 10-4 D) 1.54 10-4 H) 2.51 10-4 A) 9.81 10-2 E) 2.40 10-1 B) 1.23 10-1 F) 2.99 10-1 C) 1.53 10-1 G) 3.74 10-1 9. [5pt] The figure below shows two points in an E-field: Point 1 is at (X1,Y1) = (6,4) in m, and Point 2 is at (X2,Y2) = (13,9) in m. The Electric Field is constant, with a magnitude of 74 V/m, and is directed parallel to the +x-axis. The potential at point 1 is 1100 V. Calculate the potential at point 2 in V. Y 15. [5pt] Two identical parallel plate capacitors have plate area A = 61 cm2 and plate separation d = 1.57 mm. Initially, both are empty (have nothing between their plates). They are connected in series, and a potential difference 66 V is applied across the combination. What is the magnitude of the charge (in C) on one of the plates? A) 9.70 10-10 E) 1.82 10-9 B) 1.14 10-9 F) 2.13 10-9 C) 1.33 10-9 G) 2.49 10-9 D) 1.55 10-9 H) 2.91 10-9 2 . 1 . X 16. [5pt] The battery is then disconnected, but the capacitors remain connected to each other. The right capacitor is filled with a dielectric slab with =2.90, as shown. What is the magnitude of the potential difference (in V) across the capacitor that is filled with the dielectric material? D) -4.66 102 H) 9.09 102 A) -9.09 102 E) 4.66 102 B) -7.28 102 F) 5.82 102 C) -5.82 102 G) 7.28 102 10. [4pt] Calculate the work required to move a negative charge of Q = -608 C from point 1 to point 2 in mJ. A) -3.56 102 E) 2.47 102 B) -3.15 102 F) 2.79 102 C) -2.79 102 G) 3.15 102 D) -2.47 102 H) 3.56 102 A) 1.14 101 E) 2.87 101 B) 1.43 101 F) 3.61 101 C) 1.81 101 G) 4.55 101 D) 2.28 101 H) 5.73 101 11. [6pt] The electric potential in some region is described by the function V = x2 yez , where V is in Volts and all positions are in meters. What is the magnitude of the electric field (in V/m) at the position x = 6.0 m, y = 5.0 m, z = 0 m? A) 1.93 102 E) 3.15 102 B) 2.18 102 F) 3.56 102 C) 2.47 102 G) 4.02 102 D) 2.79 102 H) 4.54 102 17. [5pt] What is the Electric field (in V/m) inside the dielectric slab? A) 7.25 103 E) 2.10 104 B) 9.46 103 F) 2.74 104 C) 1.23 104 G) 3.58 104 D) 1.61 104 H) 4.67 104 12. [5pt] Calculate the equivalent capacitance (in F) of the circuit shown in the diagram below; where C1 = 5.65 F, C2 = 2.60 F, C3 = 1.50 F, and C4 = 3.80 F. C1 C2 C3 18. [13pt] Two semicircular rods and two short, straight rods are joined in the configuration shown. The curved rods have radii R1 and R2 . All rods carry a charge density of . Derive a formula for the potential at the center of this configuration (point P), in terms of only fundamental constants and the given variables. V C4 A) 9.33 E) 1.52 101 B) 1.05 101 F) 1.72 101 C) 1.19 101 G) 1.94 101 D) 1.35 101 H) 2.19 101 R1 P R2 Department of Physics and Astronomy, SUNY Geneseo . . . . . . . . . . . . . . . . . . . . . . CAPA c msu ...
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