PH2200 Practice Exam I Summer 2003

Transcription

1 PH00 Prctice Exm I Summer 003 INSTRUCTIONS. Write yur nme nd student identifictin number n the nswer sheet.. Plese cver yur nswer sheet t ll times. 3. This is clsed bk exm. Yu my use the PH00 frmul sheet tht is included with the exm.*. Equtins my nt be stred in clcultrs, nr my clcultrs be exchnged. 5. Recrd yur nswers in the frm A, B, C, etc, n the nswer sheet. 6. This exm cnsists f 0 cncept questins wrth fur pints ech nd five prblems hving ttl f 5 prts. The prblem prts re eqully weighted: ech is wrth fur pints. The ttl number f pints n the exm is If yu hve ny questins during the exm, plese rise yur hnd nd wit fr ssistnce. * The frmul sheet is nt included with this prctice exm.

2 PH00 Prctice Exm I Summer 003 Cncept uestins: Ech questin hs single crrect nswer nd is wrth fur pints.. Experimentl evidence indictes tht chrge is quntized nd cnserved. chrge is quntized but nt cnserved. chrge is cnserved but nt quntized. chrge is neither quntized nr cnserved. Nne f the bve.. Chse the chrges nd tht re cnsistent with the electric field lines shwn in the figure t the right. = + mc, = + mc = + mc, = - mc = - mc, = + mc = +8 mc, = + mc = -8 mc, = + mc 3. Pint chrge hs chrge f + nd pint chrge hs chrge f -. In the figures belw, the rrws represent the frce n ech sphere due t the ther sphere in tht pir. Tking bth the directin nd the length f the rrws int ccunt, which figure belw crrectly shws the electric frce tht ech pint chrge exerts n the ther?. Cnsider regulr cube with psitive pint chrge + in ll crners except fr ne which hs negtive pint chrge -. Let the distnce frm ny crner t the center f the cube be r. Wht is the mgnitude f electric field t pint P, the center f the cube? E = 0 E = ke/ r E = ke/ r E = 6 ke/ r E = 7 k / r e P + + +

3 PH00 Prctice Exm I Summer As shwn in the figure t the right, n insulting rd is net int the shpe f semicircle. The left hlf f the rd hs chrge f + unifrmly distributed lng its length, nd the right hlf f the rd hs chrge f - unifrmly distributed lng its length. Wht vectr shws the crrect directin f the electric field t pint P, the center f the semicircle? A B C D There is n electric field t pint P. + A D P B C The figure t the right pplies t the fllwing tw questins. Psitive nd negtive chrges f equl mgnitude lie lng the symmetry xis f cylinder. The distnce frm the psitive chrge t the left end-cp f the cylinder is the sme s the distnce frm the negtive chrge t the right end-cp. 6. Wht is the flux f the electric field thrugh the clsed cylinder? + right end-cp 0 + / ε + / ε / ε Nne f the bve. 7. Wht is the sign f the flux thrugh the right end-cp f the cylinder? psitive negtive There is n flux thrugh the right end-cp. 8. Which f the fllwing sttements is flse fr cnductr in electrsttic equilibrium? The electric field is zer t ll pints inside the cnductr. Any excess chrge resides entirely n the surfce. The mgnitude f the electric field due t chrged cnductr flls ff s /r where r is the distnce frm the cnductr t pint in spce utside the cnductr. The externl electric field t the surfce f chrged cnductr is perpendiculr t the surfce. The mgnitude f the externl electric field t pint n the surfce f chrged cnductr is σ / ε where σ is the surfce chrge density t tht pint. 3

4 PH00 Prctice Exm I Summer The picture t the right shws the electric field lines between tw prllel pltes tht fr ll prcticl purpses extend n infinite distnce bth t the right nd t the left nd int nd ut f the pper. Fur pints P,, R, nd S re mrked in this picture. At which pint is the electric ptentil the lrgest? P R S The electric ptentil is the sme t ll fur pints P R S 0. A psitive pint chrge is plced t the center f hllw cnductr tht is electriclly neutrl s shwn belw. Which figure best represents the electric field lines fr this system?

5 PH00 Prctice Exm I Summer 003 Prblems: Ech prt f ech prblem is wrth fur pints.. Cnsider n electric diple in unifrm electric field s shwn in the figure t the right. The diple cnsists f psitive nd 9 negtive pint chrge, ech hving mgnitude f q =.60 0 C, nd the chrges re seprted distnce f m. () Wht is the mgnitude f the electric frce tht ne chrge f the diple exerts n the ther? + q q N N 8. 0 N N N (b) Suppse the diple is relesed t rest, riented s shwn in the figure bve. Which f the fllwing sttements cncerning the mtin f the diple is crrect, ssuming the nly frce cting n the diple is the electric frce due t the unifrm electric field? The center f mss will mve, nd the diple will rtte. The center f mss will mve, but the diple will nt rtte. The center f mss will remin sttinry, but the diple will rtte. The center f mss will remin sttinry, nd the diple will nt rtte. Nne f the bve. Nw cnsider n electric diple in the nn-unifrm electric field prduced by pint chrge. As shwn in the figure t 9 the right, pint chrge f + q =.60 0 C is lcted t the rigin with the psitive nd negtive ends f the diple lcted t x = m nd x = m, respectively. P + q + q q x (c) Wht is the mgnitude f the electric ptentil t pint P lcted t x = m?.3 V.76 V 3.0 V 3.98 V.3 V (d) Wht is the mgnitude f the net frce exerted n the electric diple by the pint chrge t the rigin?.08 0 N.8 0 N.5 0 N.69 0 N.90 0 N 5

6 PH00 Prctice Exm I Summer 003. A sphericl insultr f rdius is cncentric with cnducting sphericl shell hving inner rdius 3 nd uter rdius 5 s shwn in the figure t the right. The chrge + is unifrmly distributed thrughut the vlume f the insultr, nd the net chrge n the cnductr is +. () Wht is the mgnitude f the electric field distnce f frm the center f the insultr? 0 /6πε /πε /πε + πε ( ) / + (net) (b) Wht is the flux f the electric field thrugh Gussin sphere f rdius tht is cncentric with bth the insultr nd cnducting shell? 0 / ε ( + )/ ε ( + ) / ε /6π (c) Wht is the surfce chrge density n the uter surfce f the cnductr? /00π + /00π 3 + /00π ( + )/00π /00π ( ) ( ) 6

7 PH00 Prctice Exm I Summer The visible prtin f lightning strike is preceded by n invisible stge in which clumn f electrns extends dwnwrd frm clud t the grund. Assume 3 the liner chrge density lng the clumn is.5 0 C/m. Tret the clumn f chrge s if it were stright nd infinitely lng. () Wht is the flux f the electric field thrugh clsed Gussin cylinder.00 m in length tht is cxil with the clumn f electrns? λ = C/m.00 m N m / C N m / C N m / C N m / C N m / C Gussin surfce 6 (b) At wht distnce frm the clumn f electrns des the electric field hve mgnitude f N/C? (Air underges dielectric brekdwn in n electric field exceeding this vlue, s the distnce yu clculte is n estimte f the rdius f visible lightning blt.).7 m 5.55 m 6.89 m 7.3 m 8.0 m 7

8 PH00 Prctice Exm I Summer 003. Cnsider hrizntl, insulting plne tht is unifrmly nd negtively chrged. Assume the plne is very lrge s tht edge effects my be neglected. The mgnitude f the electric field 0.00 m frm the plne 5 is.50 0 N/C. () Wht is the surfce chrge density f the plne? chrged prticle - prts (c), (d) nd (e) C/m C/m C/m. 0 C/m.3 0 C/m (b) Wht is the mgnitude f the electric ptentil difference between pint 0.00 m frm the plne nd pint 0.00 m frm the plne?.50 0 V.75 0 V V V.00 0 V 6 (c) A prticle f mss kg is bserved t be t rest 0.00 m belw the plne. Grvity cts dwnwrd in the figure, nd the mgnitude f the free-fll ccelertin is 9.80 m/s. Wht is the chrge f the prticle?.0 0 C.35 0 C.59 0 C.77 0 C.93 0 C Suppse tht the chrged prticle cquires ttl chrge f C, nd its mss remins the sme. (d) Wht is the directin f the ccelertin f the chrged prticle? up dwn Nne f the bve. (e) Wht is the mgnitude f the ccelertin f the chrged prticle? 3.0 m/s 7. m/s 0.3 m/s 5.8 m/s 33.9 m/s 8

9 PH00 Prctice Exm I Summer A cntinuus line f chrge f length 3d lies lng the x-xis, extending frm x=+ d t x=+ d. The line crries unifrm liner chrge density λ. y λ d 3d x In terms f d, λ nd ny necessry physicl cnstnts, find the mgnitude f the electric field t the rigin. λ/5πε d λ/πε d 3 λ/6πε 3 λ/8πε λ/3πε d d d 9

10 PH00 Prctice Exm I Summer 003 KEY Nme: ID# Cncept uestins Prblems A E E.. (). () B C A. (b) (b) C E A 3. (c) (c) C B A. (d) (d) C B D 5.. () (e) A A C 6. (b) 5. A D 7. (c) C C () A C 9. (b) C Subttl Subttl Subttl 3 5 Exm Scre 0