Physics 2B Spring 2010: Final Version A 1 COMMENTS AND REMINDERS:


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1 Physics 2B Spring 2010: Final Version A 1 COMMENTS AND REMINDERS: Closed book. No work needs to be shown for multiplechoice questions. 1. A charge of +4.0 C is placed at the origin. A charge of 3.0 C is then placed at x = 1.0 m. A third charge of +6.0 C is then placed at x = 10.0 m. What is the magnitude of the force on a proton placed at x = 4.0 m? a) N. b) N. c) N. d) N. e) N. 2. A uniformly charged ring is 1.0 cm in radius. The electric field on the axis 2.0 cm from the center of the ring has magnitude of 2.2 MN/C and points toward the ring center. Find the ring charge a nc b nc c nc d nc e nc 3. A closed surface contains the following point charges: 6 C, 4 C, 2 C, 4 C. The electric flux coming out of the surface is: a. 1.8 "10 12 N#m 2 b. "1.8 #10 12 N$m 2 c. 4.5 "10 11 N#m 2 d. "4.5 #10 11 N$m 2 e. 1.1"10 12 N#m 2
2 Physics 2B Spring 2010: Final Version A 2 4. Charges of C each are located at three of the corners of a square that is 1.0 m on each side. A charge of C is located at the other corner. What is the electric potential (i.e. voltage) at the center of the square due to these charges? d = 1 m a V. b V. c V. d V. e V. 5. A capacitor consists of conducting sphere of radius R 1 surrounded by a concentric conducting shell of radius R 2. What is its capacitance? a. ε ο R 12 / R 2 b. ε ο R 1.R 2 c. 4πε ο R 1.R 2 /(R 1  R 2 ) d. 4πε ο R 12 /R 2 e. ε ο (R 1  R 2 ) 6. A long, thin wire carries a uniform line charge density λ= 6.8 µc/m. It is surrounded by a thick concentric cylindrical shell of inner radius 2.5 cm and outer radius 3.5 cm. What uniform charge density in shell will result in zero electric field outside of the shell? a. 3.6 mc/m 3 b. 1.8 mc/m 3 c. 5.4 mc/m 3 d. 2.7 mc/m 3 e. 0.9 mc/m 3 7. A certain capacitor, in series with a 720 Ω resistor, is being charged by a DC battery. At the end of 10 ms its charge is half the final value. The capacitance is about: a. 9.6 µf. b. 14 µf. c. 20 µf. d. 7.2 µf. e. 10 µf.
3 Physics 2B Spring 2010: Final Version A 3 8. How much power is being dissipated by the 12Ω resistor? 16 V 4.0! a. 4.0 W b. 3.0 W c. 18 W d. 12 W e. 27 W b 18 V 8.0! 12! a 9. A metal bar has a rectangular cross section (5 cm in the x direction and 10 cm in the y direction). The current density J is uniform in the x direction but changes linearly in the y direction, going from J=0 when y=0 to J= 0.1 A/cm 2 when y=10 cm. What is the total current across the bar? a. 5.0 A. b. 1 A. c. 0.5 A. d. 2.5 A. e A. 10. What is the equivalent resistance for these resistors between points a and b? a. 7.0 Ω. b. 5.0 Ω. c. 11 Ω. d. 3.5 Ω. e. 2.5 Ω. 11. Two capacitors with capacitances of 1.5 µf and 0.25 µf, respectively, are connected in parallel. The system is connected to a 50V battery. What electrical potential energy is stored in the 1.5µF capacitor? a J b J c J d J e J
4 Physics 2B Spring 2010: Final Version A What is the equivalent capacitance between points a and b in the diagram to the right? a μf. b μf. c. 1.1 μf. d. 4.5 μf. e. 6.0 μf. 13. If a battery of 12 V is connected to this circuit of capacitors, what is the voltage on the 24 µf capacitor? a. 4 V. b. 6 V. c. 8 V. d. 3 V. e. 2 V. 20!F 12!F 24!F 12!F 14. A length of wire is formed into a closed circuit with radii a= 0.5 m and b= 1 m, as shown in the figure, and carries a current I= 10A. What is the magnitude of the magnetic field B at point P? a. 4π µt. b. π µt. c. 2π µt. d. 3π µt. e. 2 µt.
5 Physics 2B Spring 2010: Final Version A A 500 turn solenoid has a radius of 5.00 cm and a length of 20.0 cm. What is the energy stored in the solenoid when the current in its windings is 1.50 A? a mj. b mj. c mj. d mj. e mj. solenoid 16. A proton moving at a speed of m/s cuts across the lines of a magnetic field at an angle of 70. The magnitude of the magnetic field is T. What is the magnitude of the force acting on the proton? a N. b N. c N. d N. e N. 17. Three parallel wires all with the same magnitude of current (I 1 = I 2 = I 3= 10 A) are perpendicular to the plane of this page. In two of the wires, the current is directed out of the page, while in the remaining wire the current is directed into the page. What is the force per unit of length acting on wire 1? a mn/m to the right. b mn/m to the right. c. 0.5 mn/m to the left. d mn/m to the left. e mn/m to the left. 18. Two long straight wires are parallel and carry current in the opposite direction. The currents are 8.0 A and 12 A and the wires are separated by 0.40 cm. The magnitude of magnetic field at a point 0.6 cm to the right of the wire carrying the 12 A current is: a T. b T. c T. d T. e T.! 1! 2! 3 x = 4 cm 0 cm +4 cm
6 Physics 2B Spring 2010: Final Version A A square wire loop of side 0.5 m and resistance 5 Ω moves to the right with speed v = 0.25 m/s. At t=0 its rightmost edge enters a uniform magnetic field B = 1.0 T pointing into the page. Find the power dissipated by the resistor while the loop is moving into the magnetic field. a mw. b mw. c. 6.2 mw. d. 1.6 mw. e. 3.1 mw. 20. An AC voltage source, with a peak output of 200 V, is connected to a 50Ω resistor. What is the rate of energy dissipated due to heat in the resistor? a. 200 W b. 400 W c. 566 W d. 800 W e W 21. A 10.0 mh inductor and a 2.5 Ω resistor are wired in series to a 9.0 V DC battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. Find the voltage drop across the inductor after one time constant, τ L, has elapsed. a. ΔV inductor = 3.3 Volts. b. ΔV inductor = 2.3 Volts. c. ΔV inductor = 9.0 Volts. d. ΔV inductor = 5.7 Volts. e. ΔV inductor = 4.0 Volts. 22. In an RLC series circuit, the resistor has a resistance of 50 Ω, the inductor has an inductance of 0.20 H, and the capacitor has a capacitance of 150 µf. The AC source has an rms Voltage of 240 V along with a frequency of 50 Hz. What is the resonant frequency and impedance of the circuit? a. 183 Hz and 21 Ω. b. 183 Hz and 50 Ω. c. 29 Hz and 62 Ω. d. 29 Hz and 65 Ω. e. 29 Hz and 134 Ω.
7 Physics 2B Spring 2010: Final Version A 7 Recall that F = k e q 1 q 2 r 2 ; k e = 8.99"10 9 N " m 2 C 2 ; e = 1.60"10 #19 C; ε ο = 8.85!10 "12 C 2 N " m 2 ; m e = 9.11"10 #31 kg; m p = 1.673"10 #27 kg; m n = 1.675"10 #27 kg; 1 ev =1.602 "10 #19 J; 1 kwh = 3.60 "10 6 J; r r q F = q o E ; E = k e r ; " 2 E = EAcos# ; " E = Q inside qq ; PE elec,point = k 0 e # 0 r ; q V point charge = k e r ; "PE elec = q 0 "V ; C = Q "V ; C = " A parllel plate 0 d ; C = "# A dielectric 0 d ; 1 C series eq = 1 C C C 3 +K; C parallel eq = C 1 + C 2 + C 3 +K; I = "Q "t ; R = "V I = # L A ; " = " 1+ # T $ T o ( o) [ ]; R = R o [ 1+ "( T # T o )]; Power = I "V " Silver =1.59 #10 $8 %& m ; " Copper =1.7 #10 $8 %& m ( ( ) = I 2 R = "V ) 2 R ; I in = I out ; 1 R parallel eq = 1 R R R 3 +K; R series eq = R 1 + R 2 + R 3 +K; #"V loop = 0; " = RC ; q charge = Q final ( 1" e t / RC ); q discharge = Q 0 e t / RC ; db r = µ I o d r l # r ) r ; B " d r N # l = µ 4" r 2 o Icross ; µ ο = 4π 107 A ; 2
8 Physics 2B Spring 2010: Final Version A 8 r F on q = q r v " r B ; p = mv ; F cent = mv2 r I r F on I = IL r " B r ; " = BIAN sin# ; " = r F r sin# ; " = µbsin#; µ = NIA; r = mv qb ; ; B wire = µ I o 2"r ; B coil = N µ I o 2R ; B = µ solenoid o B F B! v ; left right ( N l)i ; F 1 l = µ I I o 1 2 2"d ; up down out of page into page. " B = BAcos# ; " = #N d$ B dt L = N" B I ; L = µ on 2 A l ; " = B # lv; " = NAB# sin (#t); " = 2#f ; " L = #L di dt ; ; " L = L " R ; I = Rt / L ( 1# e ); PE L = 1 2 R LI 2. I rms = I max 2 ; "V = "V max rms 2 ; P = I 2 avg rmsr; X C = 1 2"fC ; "V = I X ; X C,rms rms C L = 2"fL ; "V L,rms = I rms X L ; "V max = "V 2 R + ("V L # "V C ) 2 ; Z = R 2 + ( X L " X C ) 2 ; "V max = I max Z; tan" = X L # X C R ; P avg = I rms "V rms cos# ; I rms = "V rms Z = "V rms R 2 + X L # X C 2" LC ( ) 2 ; f o = 1 A circle = "r 2 ; A sphere = 4"r 2 ; A square = L 2 ; g = 9.80 m/s 2 ; 100 cm =1 m; 1,000 ma = 1 A; 2.54 cm =1 in; 12 in =1 ft ; 5,280 ft =1 mi; 1,609 m =1 mi; m =1 ft ; A circle = "r 2 ; A cyl. side = 2"rh ; A sphere = 4"r 2 ; g = 9.80 m/s 2 ; x = "b ± b2 " 4ac ; 100 cm =1 m; 2a 1 µf =1.0 "10 #6 F; 1 MW =1.0 "10 6 W ; 1,000 W =1 kw ; 60 s = 1 min; 60 min =1 hr; 2.54 cm =1 in; 12 in =1 ft ; 5,280 ft =1 mi; 1,609 m =1 mi; m =1 ft
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