Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes.

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1 Name Student ID II. [25 pt] Thi quetin cnit f tw unrelated part. Part 1. In the circuit belw, bulb 1-5 are identical, and the batterie are identical and ideal. Bxe,, and cntain unknwn arrangement f linear reitr. Hwever, it ha been determined that R = R > R tudent ue a vltmeter t meaure the electric ptential difference acr the three bxe. Fr the fllwing lutin: circuit I i the circuit cntaining bulb 1 and bx, circuit II i the circuit cntaining bulb 2 and the parallel netwrk f bulb 3 and bx, and circuit III i the circuit cntaining bulb 4 and the parallel netwrk f bulb 5 and bx. 17. [5 pt] The ablute value f the meaured electric ptential difference acr bx i:. Greater than that acr bx. B. Le than that acr bx. C. Equal t that acr bx. D. There i nt enugh infrmatin prvided t cmpare thee quantitie. Circuit I ha mre reitance and therefre le current thrugh the battery than circuit II (ince adding a parallel branch decreae the ttal reitance). Since the current thrugh bulb 1 i le than the current thrugh bulb 2 and the brightne f a bulb i an indicatr f current thrugh the bulb, bulb 1 i dimmer than bulb 2. Since brightne i al an indicatr f the ptential difference acr a bulb, the ptential difference acr bulb 1 i le than the ptential difference acr bulb 2, r ΔV 1 < ΔV 2. Frm Kirchhff lp rule, V bat = ΔV 1 +ΔV and V bat = ΔV 2 +ΔV, it fllw that ΔV >ΔV. 18. [5 pt] Bulb 1 i:. Brighter than bulb 2. B. Dimmer than bulb 2. C. bright a bulb 2. D. There i nt enugh infrmatin prvided t cmpare the bulb accrding t brightne. Fr the reaning decribed in quetin 17, bulb 1 i dimmer than bulb [5 pt] The ablute value f the meaured electric ptential difference acr bx i:. Greater than that acr bx. B. Le than that acr bx. C. Equal t that acr bx. D. There i nt enugh infrmatin prvided t cmpare thee quantitie. Circuit II ha a greater reitance than circuit III ince R > R. Uing the ame reaning a in quetin 23, ΔV 2 <ΔV 4. V bat = ΔV 2 +ΔV and V bat = ΔV 4 +ΔV, therefre ΔV >ΔV. Phyic 122B, utumn 2009 Final Exam EM-UW122B094L-EF(EC1,EC2)mc_ln.dc

2 Name Student ID 20. [5 pt] Bulb 3 i:. Brighter than bulb 5. B. Dimmer than bulb 5. C. bright a bulb 5. D. There i nt enugh infrmatin prvided t cmpare the bulb accrding t brightne. The ptential difference acr bulb 3 i the ame a the ptential difference acr bx, rδv 3 =ΔV. Similarly, ΔV 5 =ΔV. Since ΔV >ΔV, ΔV 3 >ΔV 5 and bulb 3 i brighter than bulb 5 (ince bulb brightne i an indicatr f the ptential difference acr a bulb). Part 2. Shwn at right i a phyical arrangement f circuit element, including ne battery, fur wire, and three bulb. 21. [5 pt] Which f the circuit diagram belw, if any, repreent the phyical arrangement f element hwn at right. B. C. D. E. Nne f the circuit hwn repreent the given phyical arrangement. E. Nne f the circuit hwn repreent the given phyical arrangement. Current frm the pitive terminal f the battery can flw (1) thrugh the wire, (2) thrugh bulb [i.e., int the threaded ide f the bae f bulb, thrugh it filament, and ut frm the tip f the bae], (3) thrugh the hrt wire cnnecting bulb and, (4) thrugh bulb, and (5) back int the negative terminal f the battery, thereby making a cmplete lp. lternatively, current may flw (1) thrugh the wire, (2) thrugh the threaded bae f bulb [imply uing it a a cnductr], (3) thrugh the wire cnnecting bulb and, (4) thrugh bulb, (5) thrugh the hrt wire cnnecting bulb and, (6) thrugh bulb, and (7) back int the negative terminal f the battery, again making a cmplete lp. In bth cae, current mut pa thrugh bulb after paing thrugh either bulb r bulb. Therefre, bulb and mut be cnnected in parallel with ne anther and bulb mut be cnnected in erie with the netwrk, a hwn at right. Phyic 122B, utumn 2009 Final Exam EM-UW122B094L-EF(EC1,EC2)mc_ln.dc

3 Name Student ID Scre III. Tw infinite inulating heet, each with the ame pitive charge denity +, interect at a right angle a hwn. Pint and B are bth a ditance t the right f the vertical heet. Pint B i al a ditance abve the hrizntal heet. The angle between path I and path III i. 23. [5 pt] Which, if any f the three path (I, II and III) are equiptential C. III nly path will be an equiptential if the electric field i perpendicular t the path at every pint. Uing uperpitin, we find that the electric field in thi cae pint up and t the right, at a angle frm the hrizntal heet. The nly path hwn that i perpendicular t thi field i path III. I B III C II 24. [5 pt] Hw de the electric ptential at pint C cmpare t the electric ptential at pint B B. The electric ptential at pint C i le than the electric ptential at pint B. Cnider a pitive pint charge that i mved alng path II, frm pint B t pint C: the path i parallel t the magnetic field at every pint, which mean the field de pitive wrk n the charge. Thu the electric ptential difference in ging frm pint B t pint C i negative, which implie that the electric ptential at B i greater than that at C. 25. [5 pt] Suppe a third identical infinite heet with charge denity + i added uch that it frm a angle with the vertical heet. Hw de V B C, the magnitude f the electric ptential difference in ging frm pint B t pint C, change with the additin f the third heet B. V B C decreae with the additin f the third heet. The electric field frm the third heet i antiparallel t and i f leer magnitude than the field frm the tw riginal heet. Uing uperpitin, we find that the reulting field till pint up and t the right at a angle frm the hrizntal heet, but i weaker than befre. Becaue the field ha maller magnitude, the wrk dne n a charge mving frm B t C will be le, which mean the magnitude f the ptential difference between the tw pint will be le. I B III C II Phyic 122B, utumn 2009 Final Exam EM-UW122B094T-EF(EPD,CHG,LN)mc_l.dc

4 Name Student ID Scre n initially neutral cnducting phere (phere ) i n an inulating tand. pitively i lwly brught near the cnducting phere, a hwn in the tp view diagram at right. The rd and phere never tuch, and n park jump between the rd and the phere. 26. [5 pt] Which f the fllwing bet decribe the net charge n phere C. The net charge n phere i zer Tp view Since the phere i ilated, and n charge wa tranferred frm r t the phere (n tuch, n park), the net charge n phere remain zer. Cae I: Tw identical initially neutral cnducting phere n inulating tand are placed uch that all three phere tuch a hwn. Cae II: pern tuche phere a hwn belw right. In bth cae, the i held tatinary, and n park jump between the rd and phere. 27. [5 pt] Che the tatement belw that bet decribe the net charge n phere in each cae.. The ign f the net charge n phere i the ame in bth cae, and i nt zer. The pitively repel the pitive charge in phere. In bth cae there i a cnducting bdy nt which the pitive charge can mve (the phere in cae I and the hand in cae II). Thu the net charge n phere i negative in bth cae. Pitively Pitively Pitively Cnducting phere n inulating tand Tp view Tp view Cae I Cae II Phyic 122B, utumn 2009 Final Exam EM-UW122B094T-EF(EPD,CHG,LN)mc_l.dc

5 Name Student ID Scre cnducting rd mve t the right with Wire cntant peed v while tuching a tatinary rectangular lp f wire, a hwn. n external unifrm, tatic magnetic field B B pint perpendicular t the plane f the lp, Directin but it directin i nt given. n induced I left unknwn current, I left, i berved t flw dwn in the left prtin f the lp frmed by the wire and v rd, a hwn. Nte: n batterie are preent. 28. [5 pt] Which f the fllwing tatement i mt crrect regarding the directin f Cnducting rd the external magnetic field B. It pint int the page. One can apply the right hand rule t the given directin f I left t btain the directin f the induced magnetic field at pint inide the left lp---it pint ut f the page. Fr definitene, ne need t che an area vectr fr the left lp. Suppe that it i chen t pint int the page. Therefre, the induced magnetic flux i negative. Frm Lenz law, ne knw that when a current i induced, it flw in uch a way that the crrepnding induced magnetic flux ppe the change in flux due t the external field. the rd mve, the left lp area increae. If the external field al pint int the page then the change in external flux ver a hrt time interval will be pitive. Thi ign i ppite t that f the induced flux a Lenz law require. 29. [5 pt] What i the directin f the magnetic frce n the rd D. T the left. Frm quetin 28 ne knw that the external field pint int the page. The current in the rd i up. [T ee thi, ne may apply the frce law F = qv B t a pitive charge carrier, which i initially tatinary relative t the rd, t get the directin f charge flw. l, nte that current up the rd generate a magnetic field that pint ut f the page at pint inide the plane f the left lp, jut a the field due t I left de.] The magnetic frce n the current-carrying rd i given by F = I rd L B, where L pint up the rd. The cr prduct yield a frce vectr that pint t the left. 30. [5 pt] the rd i mving, there will be a nnzer induced current I rd thrugh the rd and an induced current I right thrugh the right prtin f the lp. Hw d their magnitude cmpare B. I rd i alway greater than I right. Frm quetin 28 ne knw that the external field pint int the page. If the area vectr fr the right lp i taken a pinting int the page, then the change in external flux i negative ver a hrt time interval. Frm Lenz law, ne knw that the induced current I right flw clckwie in the right lp ince thi cntribute a pitive flux. The current in the rd flw up alng the rd. Thu, at the tp junctin where the rd and wire tuch, I rd = I left + I right. By cntructin, thee current repreent pitive charge flw. Since I left i nn-zer, it mean that I rd i alway greater than I right. Phyic 122B, utumn 2009 Final Exam EM-UW122B094T-EF(EPD,CHG,LN)mc_l.dc

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