AP Physics C: Electricity and Magnetism

Transcription

1 08 AP Physcs C: Electcty n Mgnetsm Fee-Response Questons 08 The College Bo. College Bo, Avnce Plcement Pogm, AP, AP Centl, n the con logo e egstee temks of the College Bo. Vst the College Bo on the Web: AP Centl s the offcl onlne home fo the AP Pogm: pcentl.collegebo.og.

2 Poton mss, Neuton mss, Electon mss, Avogo s numbe, ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION m p m n m e CONSTANTS AND CONVERSION FACTORS kg kg kg 3 N mol Unvesl gs constnt, R 8.3 J (mol K) 3 Boltzmnn s constnt,.38 0 J K k B Electon chge mgntue, 9 e.60 0 C 9 electon volt, ev.60 0 J 8 Spee of lght, c m s Unvesl gvttonl G Nm kg Acceleton ue to gvty t Eth s sufce, constnt, g 9.8 m s 7 unfe tomc mss unt, u.66 0 kg 93 MeV c Plnck s constnt, 34 5 h J s evs 5 3 hc.99 0 J m.4 0 evnm Vcuum pemttvty, Coulomb s lw constnt, k pe0 Vcuum pemeblty, e C Nm N m C 7 m0 4p 0 (Tm) A 7 Mgnetc constnt, k m0 4p 0 (Tm) A 5 5 tmosphee pessue, tm.0 0 N m.0 0 P UNIT SYMBOLS mete, klogm, secon, mpee, kelvn, m kg s A K mole, hetz, newton, pscl, joule, mol Hz N P J wtt, coulomb, volt, ohm, heny, W C V W H f, tesl, egee Celsus, electon volt, F T C ev PREFIXES Fcto Pefx Symbol 9 0 gg G 6 0 meg M 3 0 klo k 0 cent c 3 0 mll m 6 0 mco m 9 0 nno n 0 pco p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q snq cosq tnq The followng ssumptons e use n ths exm. I. The fme of efeence of ny poblem s netl unless othewse stte. II. The ecton of cuent s the ecton n whch postve chges woul ft. III. The electc potentl s zeo t n nfnte stnce fom n solte pont chge. IV. All bttees n metes e el unless othewse stte. V. Ege effects fo the electc fel of pllel plte cpcto e neglgble unless othewse stte. --

3 ADVANCED PLACEMENT PHYSICS C EQUATIONS à x Ãx0 t x x x0 Ãx0t xt Ãx Ãx0 xx x0 F F net m m p F t J Ft Dp p mv F f m F N D E W F K mã P E t P Fv DUg à c mgdh w t F t t I I net I m m x cm mx m à w L p Iw K Iw w w 0 t q q0 w0t t MECHANICS = cceleton E = enegy F = foce f = fequency h = heght I = ottonl net J = mpulse K = knetc enegy k = spng constnt = length L = ngul momentum m = mss P = powe p = momentum = us o stnce T = peo t = tme U = potentl enegy v = velocty o spee W = wok one on system x = poston m = coeffcent of fcton q = ngle t = toque w = ngul spee = ngul cceleton f = phse ngle F kdx s U s k x D x x mx cos( wt f T T p w f s T p F U G G p p m k g Gm m Gm m ELECTRICITY AND MAGNETISM qq A = e FE 4pe B = mgnetc fel 0 C = cpctnce F = stnce E E q E = electc fel e = emf Q F = foce E A e 0 I = cuent J = cuent ensty V Ex L = nuctnce x = length D n = numbe of loops of we V E pe unt length N = numbe of chge ces q V pe unt volume 4pe 0 P = powe Q = chge qq U q = pont chge E qv 4pe0 R = esstnce = us o stnce DV Q t = tme C U = potentl o stoe enegy ke 0 A V = electc potentl C v = velocty o spee = esstvty Cp C F = flux k = electc constnt Cs C F M qv B Q I B m I 0 t U m 0 I C QDV C DV B 4p R F A I B B E J s m0ni I Nev A FB B A D I V F e R B E t R s R R R p P IDV I e L t UL LI -3-

4 ADVANCED PLACEMENT PHYSICS C EQUATIONS GEOMETRY AND TRIGONOMETRY CALCULUS Rectngle A bh Tngle A Ccle bh A p C p s q Rectngul Sol V wh Cylne V p S p p Sphee 4 V p 3 S 4p 3 Rght Tngle A = e C = ccumfeence V = volume S = sufce e b = bse h = heght = length w = wth = us s = c length q = ngle s q f f u x u x n x nx n x e x x e x ln x x x snx cosx x cosx snx x n n x x x, n n e x x e x x ln x x cosxx snx sn x x cos x b c snq c b cosq c tnq b q c b 90 VECTOR PRODUCTS AB ABcosq A B ABsnq -4-

5 08 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS PHYSICS C: ELECTRICITY AND MAGNETISM SECTION II Tme 45 mnutes 3 Questons Dectons: Answe ll thee questons. The suggeste tme s bout 5 mnutes fo nsweng ech of the questons, whch e woth 5 ponts ech. The pts wthn queston my not hve equl weght. Show ll you wok n ths booklet n the spces pove fte ech pt.. A sol plstc sphee of us n conuctng sphecl shell of nne us b n oute us c e shown n the fgue bove. The shell hs n unknown chge. The sol plstc sphee hs chge pe unt volume gven by ρ( )= β, whee β s postve constnt n s the stnce fom the cente of the sphee. Expess you nswes to pts (), (b), n (c) n tems of β,,, n physcl constnts, s ppopte. () Conse Gussn sphee of us concentc wth the plstc sphee. Deve n expesson fo the chge enclose by the Gussn sphee fo the followng egons.. <. < <b (b) Use Guss s lw to eve n expesson fo the mgntue of the electc fel n the followng egons.. <. < <b (c) At ny pont outse of the conuctng shell, t s obseve tht the mgntue of the electc fel s zeo.. Detemne the chge on the nne sufce of the conuctng shell. Justfy you nswe.. Detemne the chge on the oute sufce of the conuctng shell. 08 The College Bo. Vst the College Bo on the Web: GO ON TO THE NEXT PAGE.

6 08 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (). On the xes below, sketch the electc fel E s functon of stnce fom the cente of the sphee. Sketch the gph fo the nge = 0 t the cente of the sphee to = c t the outse of the conuctng shell.. The fgue below shows the sphee n shell wth fou ponts lbele W, X, Y, n Z. Pont W s t the cente of the sphee, pont X s on the sufce of the sphee, n ponts Y n Z e on the nne n oute sufce of the shell, espectvely. Rnk the ponts ccong to the electc potentl t tht pont, wth nctng the lgest electc potentl. If two ponts hve the sme electc potentl, gve them the sme numecl nkng. W X Y Z 08 The College Bo. Vst the College Bo on the Web: GO ON TO THE NEXT PAGE.

7 08 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS. An expement s esgne to mesue the electc constnt of ppe tht hs n e A = m. Usng lumnum fol, two pllel pltes e cete wth the sme e s the ppe. Fve hune sheets of ppe e plce between the lumnum fol pltes to cete pllel plte cpcto, s shown n the fgue bove. Usng multmete, the cpctnce C of the cpcto s mesue. The numbe of sheets n the totl thckness of the stck of ppe e ecoe. The expement s epete, eucng the numbe of sheets of ppe ech tme. The t e ecoe n the tble below. Sheets of Ppe (m) C (F) () Incte below whch qunttes shoul be gphe to yel stght lne whose slope coul be use to clculte numecl vlue fo the electc constnt of the ppe. Vetcl xs: Hozontl xs: Use the emnng columns n the tble bove, s neee, to eco ny qunttes tht you ncte tht e not gven. Lbel ech column you use n nclue unts. 08 The College Bo. Vst the College Bo on the Web: GO ON TO THE NEXT PAGE.

8 08 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (b) Plot the t ponts fo the qunttes ncte n pt () on the gph below. Clely scle n lbel ll xes, nclung unts f ppopte. Dw stght lne tht best epesents the t. (c) Usng the stght lne, clculte electc constnt fo the ppe. The stuent now mkes cpcto usng the sme lumnum fol pltes n just one sheet of ppe. Usng the expementlly etemne electc constnt, the stuent clcultes the cpctnce to be 8 nf. The stuent uses ths unchge cpcto to bul ccut usng we, 36 V bttey, 3 entcl 80 Ω esstos, n n open swtch, s shown n the fgue bove. () Clculte the cuent n the bttey mmetely fte the swtch s close. (e) Detemne the tme constnt fo ths ccut. (f) Stuents A n B mesue the tme t tkes fte the swtch s close fo the voltge coss the cpcto to ech hlf ts mxmum vlue n fn tht t s longe thn expecte.. Stuent A ssumes tht the cpctnce vlue s coect. Woul Stuent A conclue tht the esstnce vlue s lge o smlle thn mesue? Lge thn mesue Smlle thn mesue Expln expementlly wht coul ccount fo ths.. Stuent B ssumes tht the esstnce vlue s coect. Woul Stuent B conclue tht the cpctnce vlue s lge o smlle thn mesue? Lge thn mesue Smlle thn mesue Expln expementlly wht coul ccount fo ths. 08 The College Bo. Vst the College Bo on the Web: GO ON TO THE NEXT PAGE.

9 08 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS 3. The fgues bove epesent ffeent vews of two long, stght, hozontl wes, n, cyng cuents I = I n I = I, espectvely, n the ectons shown. The wes e hel n plce. In Fgue, the cuent n we s ecte out of the pge, n we s stnce bove we. Pont P s hozontl stnce fom we n stnce ectly bove we. Expess you nswes to pts () n (b) n tems of I,, n physcl constnts, s ppopte. () Use Ampee s lw to eve n expesson fo the mgntue of the mgnetc fel t pont P ue to we. (b) Deve n expesson fo the mgntue of the net mgnetc fel t pont P. (c) Clculte the numecl vlue of the ngle to the hozontl fo the ecton of the net mgnetc fel t pont P. () We s now elese. Whch of the followng best escbes the ntl moton of we ue to the mgnetc fel of we? Assume gvttonl effects e neglgble. We wll not move. We wll move upw s vewe n Fgue. We wll move ownw s vewe n Fgue. We wll otte clockwse s vewe n Fgue. We wll otte counteclockwse s vewe n Fgue. Justfy you nswe. 08 The College Bo. Vst the College Bo on the Web: GO ON TO THE NEXT PAGE.

10 08 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS We s now eplce by conuctng ectngul loop of length, wth w, n esstnce R. The loop s plce stnce fom we, s shown. The loop, we, n stnce e ll n the plne of the pge. The long se of the loop s pllel to the we. The cuent I fo we s ecesng lnely s functon of tme t ccong to the equton I = I 0 ( kt), whee k s postve constnt wth unts of s -. (e) Of the followng, select the ntegton tht wll gve n expesson fo the flux Φ s functon of tme t. = + w μ 0 (I kt 0 )( ) w Φ= π = = w μ 0 (I 0 )( kt) w Φ= π = = + w μ 0 (I 0 )( kt) Φ= π = = w μ 0 (I 0 )( kt) Φ= π (f) Gven tht the flux though the ectngul loop s functon of tme t s gven by the equton μ I ( kt ) + w Φ= 0 0 ln, eve n expesson fo the mgntue of the cuent, f ny, nuce n the π ( ) loop. Expess you nswes n tems of I 0,,, R, w, k,, n physcl constnts, s ppopte. (g) Wht s the ecton of the cuent, f ny, nuce n the loop s seen n Fgue 3? Clockwse Counteclockwse = Unefne, becuse thee s no cuent nuce n the loop Justfy you nswe. STOP END OF EXAM 08 The College Bo. Vst the College Bo on the Web: -0-