Instructor(s): Acost/Woodrd PHYSICS DEPATMENT PHY 049, Fll 015 Midterm 1 September 9, 015 Nme (print): Signture: On m honor, I hve neither given nor received unuthorized id on this emintion. YOU TEST NUMBE IS THE 5-DIGIT NUMBE AT THE TOP OF EACH PAGE. DIECTIONS (1) Code our test number on our nswer sheet (use 76 80 for the 5-digit number). Code our nme on our nswer sheet. Drken circles completel (errors cn occur if too light). Code our student number on our nswer sheet. () Print our nme on this sheet nd sign it lso. (3) Do ll scrtch work nwhere on this em tht ou like. At the end of the test, this em printout is to be turned in. No credit will be given without both nswer sheet nd printout with scrtch work. (4) Work the questions in n order. Incorrect nswers re not tken into ccount in n w; ou m guess t nswers ou don t know. (5) If ou think tht none of the nswers is correct, plese choose the nswer given tht is closest to our nswer. (6) Blcken the circle of our intended nswer completel, using number pencil. Do not mke n str mrks or the nswer sheet m not red properl. Completel erse ll incorrect nswers, or tke new nswer sheet. (7) As n id to the eminer (nd ourself), in cse of poorl mrked nswer sheets, plese circle our selected nswer on the emintion sheet. Plese remember, however, tht in the cse of disgreement, the nswers on the bubble sheet count, NOT wht ou circle here. Good luck!!! >>>>>>>>WHEN YOU FINISH <<<<<<<< Hnd in the nswer sheet seprtel. Constnts ǫ 0 = 8.85 10 1 F/m m e = 9.11 10 31 kg m p = m n = 1.67 10 7 kg e = 1.6 10 19 C k = 9 10 9 N m /C µ 0 = 4π 10 7 T m/a N A = 6.0 10 3 toms/mole c = 3 10 8 m/s m = milli = 10 3 µ = micro = 10 6 n = nno = 10 9 p = pico = 10 1 1. Two ver lrge, nonconducting plstic sheets, ech 10 cm thick, crr uniform chrge densities σ 1, σ, σ 3, nd σ 4 on their surfces s shown in the figure. These surfce chrge densities hve the vlues (in µc/m ): σ 1 = 6, σ = 4, σ 3 =, nd σ 4 = 1. Find the mgnitude of the electric field t point B, fr from the edges of these sheets. (1) 1.7 10 5 N/C () 5.6 10 4 N/C (3).8 10 5 N/C (4) 7.3 10 5 N/C (5) 0 N/C σ 1 σ σ 3 σ 4 A B C 10 cm 1 cm 10 cm. Two ver lrge, nonconducting plstic sheets, ech 10 cm thick, crr uniform chrge densities σ 1, σ, σ 3, nd σ 4 on their surfces s shown in the figure. These surfce chrge densities hve the vlues (in µc/m ): σ 1 = 6, σ = 4, σ 3 =, nd σ 4 = 1. Find the mgnitude of the electric field t point A, fr from the edges of these sheets. (1) 5.6 10 4 N/C () 1.7 10 5 N/C (3).8 10 5 N/C (4) 7.3 10 5 N/C (5) 0 N/C σ 1 σ σ 3 σ 4 A B C 10 cm 1 cm 10 cm
3. A ver smll object with mss 8 10 9 kg nd positive chrge 6 10 9 C is projected directl towrd ver lrge insulting sheet of positive chrge tht hs uniform surfce chrge densit of 5 10 8 C/m. The object is initill 0.5 m from the sheet, nd its initil speed is 40 m/s. Wht is the distnce of closest pproch to the sheet? (1) 0.1 m () 0.1 m (3) 0.31 m (4) 0.38 m (5) 0 m 4. A hollow, conducting sphere with n outer rdius of 0.5 m nd n inner rdius of 0.5 m hs uniform surfce chrge densit of+3 10 6 C/m. A chrgeof 3µCis nowintroduced into the center ofthe cvitinside the sphere. Clculte the mgnitude of the electric field just outside the sphere. (1).3 10 5 N/C () 4.5 10 5 N/C (3) 3.4 10 5 N/C (4) 1.1 10 5 N/C (5) 0 N/C 5. Wht is the net enclosed chrge in the shown cube if the electric field is given b E = 4î+( )ĵ nd the cube hs side length of 4? (1) 64ǫ 0 () 0 (3) 4ǫ 0 (4) 18ǫ 0 (5) 3ǫ 0 z 6. Wht is the net enclosed chrge in the shown cube if the electric field is given b E = 4î+( )ĵ nd the cube hs side length of 4? (1) 18ǫ 0 () 0 (3) 4ǫ 0 (4) 64ǫ 0 (5) 3ǫ 0 z 7. Two identicl rindrops, ech with rdius of 1 mm nd chrge of.8 10 1 C, collide nd merge into one lrger nd sphericl rindrop. Wht is the potentil t the surfce of this merged rindrop if its chrge is distributed over its volume? (1) 40 V () 5 V (3) 50 V (4) 0 V (5) 1.5 V 8. Two identicl rindrops, ech with rdius of 1 mm nd chrge of 1.4 10 1 C, collide nd merge into one lrger nd sphericl rindrop. Wht is the potentil t the surfce of this merged rindrop if its chrge is distributed over its volume? (1) 0 V () 5 V (3) 50 V (4) 40 V (5) 1.5 V 9. In certin region of spce, the electric potentil is V(,,z) = A B + C, where A, B, nd C re positive constnts. At which of the following points is the electric field equl to zero? (1) = AC/B, = C/B, z = 0 () = 0, = 0, z = 0 (3) = A/(B C), = 1, z = 0 (4) = BC/A, = C/A, z = 0 (5) = AC/B, = C/B, z = 0
10. How much work is required (s mesured in ev) to ssemble three electrons into n equilterl tringle with side length of 10 9 m? The electrons re initill seprted infinitel fr from one nother. (1) 4.3 ev () 1.4 ev (3) 4.3 10 9 ev (4).3 10 19 ev (5).9 ev 11. A chrged glss rod is bent into the shpe of semicircle of rdius nd hs liner chrge densit of λ. Wht is the potentil t point C t the center of the semicircle? (Tke V = 0 infinitel fr w.) λ (1) λ/(4ǫ 0 ) () λ/(4πǫ 0 ) (3) λ/(πǫ 0 ) (4) λ/(ǫ 0 ) (5) 0 C 1. Three prticles re fied on the is. Prticle 1 of chrge q 1 is t =, nd prticle of chrge q is t = +. If their net electrosttic force on prticle 3 of chrge +Q is to be zero, wht must be the rtio q 1 /q when prticle 3 is t = 1.5? (1) 5 () 9 (3) 1 (4) +9 (5) +5 13. Three identicl conducting spheres initill hve the following chrges: sphere A, +4Q; sphere B, 6Q; nd sphere C, 0. Sphere A nd B re fied in plce with center-to-center seprtion tht is much lrger thn the spheres. Two eperiments re conducted. In eperiment 1, sphere C is touched to sphere A nd then (seprtel) to sphere B, nd then it is removed. In eperiment, strting with the sme initil sttes, the procedure is reversed: sphere C is touched to sphere B nd then (seprtel) to sphere A, nd then it is removed. Wht is the rtio of the electrosttic force between A nd B t the end of eperiment to tht t the end of eperiment 1? (1) 3/8 () 8/3 (3) 1/1 (4) 4/1 (5) 1/4 14. Four prticles form squre s shown. The chrges re q 1 = q 4 = Q nd q = q 3 = q. Wht is Q/q if the net electrosttic force on prticles 1 nd 4 is zero? (1) 8 () + 8 (3) (4) +/ (5) 1 1 3 4 15. The figure shows plstic ring of rdius = 50.0 cm. Two smll chrged beds re on the ring. Bed 1 of chrge +.00 µc is fied in plce t the left side; bed of chrge +6.00 µc cn be moved long the ring. The two beds produce net electric field of mgnitude E =.00 10 5 N/C t the center of the ring. Wht is the ngle θ in degrees? ing Bed 1 θ Bed (1) 67.8 (). (3) 0.7 (4) 69.3 (5) 53.1
16. The figure shows three circulr rcs centered on the origin. On ech rc, the uniforml distributed chrge is given in terms of Q =.00 µc. The rdii re given in terms of = 10.0 cm. Wht is the vlue of the component of the electric field (in 10 6 N/C) t the origin? (1) +1.14 () 1.14 (3) 0 (4) +1.80 (5) 1.80 +9Q 4Q +Q 3 17. A nonconducting rod of length L = 8.15 cm hs chrge q = 4.3 fc uniforml distributed long its length. Wht is the mgnitude of the electric field (in 10 3 N/C) produced t point P distnce = 1.0 cm from the rod? L q P (1) 1.57 () 0.94 (3).64 (4) 8.3 (5).64 18. The line lbelled 1 on figure () gives the chrge q tht cn be stored on cpcitor 1 versus the electric potentil V set up cross it. The verticl scle is set b q s = 16.0 µc, nd the horizontl scle is set b V s =.0 V. The lines lbelled nd 3 re similr plots for cpcitors nd 3, respectivel. Figure b shows circuit with these three cpcitorsnd 6.0 Vbtter. Wht is the chrge (in µc) stored on cpcitor in tht circuit? (1) 1 () 4 (3) 16 (4) 3 (5) 8 q(µc) q s 0 V(V) () V s 1 3 C 1 V C C 3 (b) 19. The prllel pltes in cpcitor, with plte re of 8.50 cm nd n ir-filled seprtion of 3.00 mm, re chrged b 6.00 V btter. The re then disconnected from the btter nd pulled prt (without dischrge) to seprtion of 8.00 mm. Neglecting fringing, wht is the potentil difference between the pltes? (1) 16 V () 6 V (3) V (4) 1 V (5) 8 V 0. The spce between two concentric conducting sphericl shells of rdii b = 1.70 cm nd = 1.0 cm is filled with substnce of dielectric constnt κ = 3.5. A potentil difference of V = 73.0 V is pplied cross the inner nd outer shells. Wht is the free chrge (in nc) on the inner shell? (1) 7.78 () 7.45 (3) 0.33 (4).9 (5) 3.4 1. A 9.00 V btter is connected to resistive strip tht consists of three sections with the sme cross-sectionl res but different conductivities. The grph shows the electric potentil V() versus position long the strip. The horizontl scle is set b s = 8.00 mm. Section 3 hs conductivit 3.00 10 7 (Ωm) 1. Wht is the conductivit of section 1 in units of 10 7 (Ωm) 1? V () = 0 = s V(V) (b) 8 6 4 0 1 (mm) 3 s (1) 6 () 4 (3) 1 (4) (5) 1/. A certin wire hs resistnce. Wht is the resistnce of second wire, mde of the sme mteril, tht is hlf s long nd hs hlf the dimeter? (1) () (3) / (4) 4 (5) /4
3. Wire C nd D re mde from different mterils nd hve length L C = L D = 1.0 m. The resistivit nd dimeter of wire C re.0 10 6 Ωm nd 1.00 mm, nd those of wire D re 1.0 10 6 Ωm nd 0.50 mm. The wires re joined s shown, nd current of.0 A is set up in them. Wht is the rte t which energ is dissipted in wire C? C L C D L D 1 3 (1) 10 W () 0 W (3) 8 W (4) 3 W (5) 16 W FOLLOWING GOUPS OF QUESTIONS WILL BE SELECTED AS ONE GOUP FOM EACH TYPE TYPE 1 Q# S 1 Q# S TYPE Q# S 5 Q# S 6 TYPE 3 Q# S 7 Q# S 8