E Problems for Unit I

Transcription

1 Physics 212E Chowry Clssicl n Moern Physics Spring 2005 E Problems for Unit I E1: Chrge Blloon. Chrge up blloon, n etermine whether it hs T chrge or B chrge. Describe your experiment. Next, ischrge the blloon (or blow up nother one); verify tht this blloon is overll neutrl. (How cn you etermine if the blloon is neutrl?) See if you cn chrge up the blloon so tht it hs n opposite sign chrge to your first cse. Describe your ttempts to chrge the blloon with opposite sign. Feel free to iscuss your ttempts t the Discussion Bor t the course web-site. E2: Visulizing Electric Fiels. The following web exercises will give you prctice with the electric fiel from vrious configurtions of chrges (both fiel lines n fiel vectors). The first one is from Slt Lke Community College, n the secon one from the Dvison College Physlets site. ) Go to n ply roun with ifferent configurtions of chrges (points of tringle, corners of squre, positive vs. negtive, ifferent mgnitues) n see the vrious kins of electric fiel lines you cn obtin. You my ignore Drw n equipotentil line n Auto rw electric potentil lines. b) Go to Work through problems 1, 2, 3, n 4. This is ifferent from the previous exercise in tht you cn see the mgnitue n irection of the fiel vector t given points. c) Go to (This is just problem 4 from prt b gin.) Increse the seprtion istnce between the poles of the ipole by bout twice. Consier the line connecting the two chrges. Move the re ot long tht line, strting from left of the positive chrge, to the mile of the chrges, n ening to the right of the negtive chrge. Wht interesting things o you notice? ) Continues from prt c). Now, consier the perpeniculr line tht bisects the line segment connecting the poles of the ipole. Move the re ot from the center of the ipole out long tht perpeniculr bisector. Wht o you notice bout the length of the rrow? E3: Chrges on Strings. Three (point like) chrges: +q, +2q, n +4q re connecte by (mssless, inextensible) strings s shown in the figure below, with seprtion istnce between nerest neigbors. Fin the tension in ech string. +q +2q +4q E4: Prty Blloons. Blloons on the wlls t prty look festive. Blloons on the floor t prty get stompe. To prevent blloon stomping, you chrge up blloon by rubbing it through your hir or on some clothes; the blloon will then stick to the wll. Explin using wors n crtoon sketches why chrge blloon will stick to wll, even though the wll likely oes not hve ny net chrge. E5: Electron Orbit. A simple moel of hyrogen tom hs the electron moving in circulr orbit bout sttionry proton (protons re bout 2000 times more mssive thn electrons). The centripetl force is provie by the electrosttic force of ttrction between the proton n the electron. The electron hs kinetic energy 2.18 x J. () Wht is the spee of the electron? (b) Wht is the rius of the orbit of the electron? Note: lter in the semester, we ll evelop better moels for toms tht utilize quntum mechnics.

2 E6: Electric Fiels through Integrtion Semi-infinite ro I. In the figure to the right, point P is locte on the positive x- xis, istnce from the origin. A semi-infinite ro with (uniform) liner chrge ensity λ > 0 begins t the origin n extens long the negtive y-xis, s shown. ) Set up n evlute the integrl tht will llow you to clculte the x-component of the electric fiel t the point P. b) Set up n evlute the integrl tht will llow you to clculte the y-component of the electric fiel t the point P. c) Wht interesting (n likely surprising) thing o you notice bout the mgnitues of the x- n y- components of the electric fiel t this prticulr point P? y P x E7: Electric Fiels through Integrtion Arcs. The figure to the right shows n rc of rius R in the x-y plne running from θ = 0 to θ = π, which crries liner chrge ensity λ. ) Assume tht λ is positive n uniform. Set up n evlute the integrls tht will llow you to etermine the x- n y- components of the electric fiel t the point P, which is t the origin. Though you my be ble to use symmetry rgument for one of the components, plese explicitly evlute the integrls to verify your intuition. b) Now, ssume tht the chrge ensity λ epens on the ngle θ such tht λ = λ0 cos θ (with λ0 positive). Set up n evlute the integrls tht will llow you to etermine the components of the electric fiel t the origin. E8: Flux through Cube. A positive point chrge q is t the center of cube of sie length L. Determine the net outwr flux of the electric fiel through the entire cubic surfce, n etermine the flux through just one fce of the cube. Which of your nswers woul chnge if the chrge weren t t the center of the cube? E9: Electric Fiels through Integrtion Semi-infinite ro II. In the figure to the right, point P is locte in the first qurnt, istnce to the right of the origin, n istnce bove the origin. A semiinfinite ro with negtive (uniform) liner chrge ensity begins t the origin n extens long the negtive y-xis, s shown. Set up n evlute the integrl to clculte the x-component of the electric fiel t the point P. E10: Electron Orbit, Revisite. An erly moel of the hyrogen tom consiere the tom to consist of proton (trete s uniformly chrge sphere of rius R), with the electron (mss m) in n orbit of rius r0 tht ws ctully insie the proton, s shown in the figure. ) Use Guss s lw to obtin the mgnitue of E (the fiel ue to the proton) t the position of the electron. Give your nswer in terms of e (the chrge on the proton), r0 n R s well s ny funmentl constnts. b) Obtin n expression for the frequency of revolution f in terms of ny of the givens m, e, R, r0 n ny funmentl constnts. y R P r0 Electron x Proton

3 E11: Constnt Potentil Prllel Pltes. The sketch shows three lrge prllel plte conuctors hel t the potentils shown. V = -30V +50V +20V 5 cm 10 cm ) Fin the irection n mgnitue of the uniform electric fiel in ech of the two interior regions. How o you know the electric fiel is uniform? b) An electron is relese from rest exctly hlf wy in between the + 50 V plte n the +20 V plte. Which plte oes the electron he towr? c) Wht spee oes this electron hve when it collies with the plte it is moving towrs? E12: Let There Be Light (Bulbs). In lb, for Experiment 13: Circuits, you plye with some btteries, light bulbs, n wires. You hve ll those in your kits. Plce the btteries in the bttery holer n bulb in the bulb holer. ) Mke circuit with the one of the les from the bttery cse connecte in series to n lligtor clip le connecte in series to light bulb connecte in series to the other le from the bttery cse. Note the brightness. Now full length of one of your nichrome wires (bre silvery wire) to your circuit between the positive sie of your btteries n the bulb. Wht hppens to the brightness of the bulb? Explin briefly. b) Repet with the other equl piece of nichrome wire, using the sme length you use in the previous prt. Which wire hs lrger resistnce? A lrger resistivity? Explin how you know. Exmine the two wires crefully. Do you note ny ifference? c) Now use just the higher resistnce wire in the circuit. Crefully unclip the le on the wire nerest the bttery, n touch it onto the wire t vrious plces. How is the bulb s brightness ffecte? This is bsiclly how immer switch works! ) Now, mke nother circuit s in prt ), but this time with two bulbs in series. Note the brightness. e) Now replce one of the bulb holers in the circuit with the higher resistnce nichrome wire, n slie the lligtor le from the btteries long the wire (reucing the length of the prt of the wire in the circuit) until the remining bulb is bout s bright s before with the two bulbs. This mens the resistnce of tht length of nichrome is the sme s bulb. Mesure this length. f) Since the wire is known to hve imeter of 0.25 mm, you cn look up the resistivity of the wire in the text, n clculte the resistnce of the wire, n therefore of the bulb. g) From the bttery voltge n the resistnce of one bulb, etermine the current through norml flshlight bulb tht uses two D-btteries (ssume the btteries hve the voltge they re lbele with).

4 E13: Do the Twist. Tke your two (very strong!) cylinricl br mgnets from your toy kits. ) Ply with the mgnets. If you on t think they re wesome, you must be e insie. Write own some of the wesome things you i with these mgnets. Don t write own if you i nything illegl or immorl. If you in t fin nything wesome to o with these mgnets, write own why you re e insie. Post your responses to the Discussion Bor t the course web-site. b) Tke out the piece of string from your kit, n put the mgnets together so tht they squeeze the string in between them n re suspene from the string. Gently put one finger to the mgnets so tht they come to rest. When t rest, o the mgnets hve preferre orienttion? Check this by isplcing them slightly from their equilibrium position or by slightly twisting the string. Why might these mgnets hve preferre orienttion? c) We si tht mgnetic moment in n externl mgnetic fiel woul unergo torque tht tene to lign the mgnetic moment with the externl fiel. Fin someone else with mgnet, n test this out. Remember tht the fiel lines from br mgnet go out the North pole en n come in the South pole en. E14: Mpping Mgnetic Fiel Lines. Get your cylinricl br mgnet n plce it, lying own (long xis horizontl), on piece of pper. Use your compss to etermine the re pole n the white pole of the br mgnet. ) Now, leving the br mgnet on the pper, trce out the mgnet (it shoul look like little rectngle) n inicte the re pole n the white pole on your rwing. Next, preict n sketch the mgnetic fiel ue to the br mgnet by rwing little x s t vrious points on the pper n inicting the irection of the mgnetic fiel using rrows. b) Plce your compss t the vrious x s n rw sketch of wht you observe. Y our sketch for the compss shoul hve little circle with n rrow crefully showing the irection the re prt of the compss neele ws pointing. c) Your preicte rrows from prt ) n the experimentlly etermine rrows from prt b) shouln t be perfectly ligne. How come? (Hint: consier wht the purpose of compss is, n how it ccomplishes this.) E15: Repulsion Rce. Consier proton n n lph prticle (which is nucleus consisting of two protons n two neutrons) initilly hel 1 nm prt t rest. ) The proton n lph prticle re relese from rest n move wy from ech other. Assume the prticles only interct with ech other when relese. When they re very fr prt, the proton is moving 4 times s fst s the lph prticle. Explin, using conservtion lw, why this must be the cse. b) Determine the finl spee of the proton when it is very fr wy from the lph prticle.

5 E16: Mgnetic Home? We ve seen tht currents re source of mgnetic fiels by looking t the eflection of compss neele ue to current in wire. Your orm room, clss rooms, n houses contin lots of wires crrying current through them. Do you nee to be concerne bout ll the mgnetic fiels from power lines in your home? ) The wire to 100 Wtt lmp crries bout 1 mp of current to light the lmp. Clculte the mgnetic fiel 5 mm from wire crrying stey current of 1 mp. Compre this to the Erth s fiel of pproximtely 0.7 G ( = 7 x 10 5 T). b) Put your compss ner vrious wires in your room leing to electricl pplinces n lights. Describe the compss eflections. Why on t you see much? (Hint: you ve probbly notice tht ll plugs hve t lest two prongs; wht o you think these two prongs re for?) E17: C mon, Bby, Light My. Light Bulb? Let s see if we cn use Fry inuction to light light bulb, using moving mgnet. ) Mke circuit consisting of light bulb n one lligtor le. Hook both ens to the light bulb so tht the wire mkes circle. Ly your circuit on the tble n wve your mgnet over it with the north pole pointing own. Be sure the mgnet moves from irectly over the circuit to t lest foot wy from bove the center of the circuit. Does the bulb light? b) The mgnetic fiel t the north pole of the mgnet coul be s strong s 0.1 T, but it is only this lrge over n re the size of the circulr mgnet en fce. Estimte this re n the time it tkes to move from flux to no flux, n thus estimte the inuce emf. Use this to explin your nswer to prt ). c) In lb, uring Experiment 15: Motors n Genertors, you were ble to light up specil kin of light bulb ( Light Emitting Dioe, or LED). Discuss t lest two importnt things tht were ifferent between wht you i in prt ) n wht you i in lb tht resulte in getting the LED to light up. E18: Current Loop s Mgnetic Dipole. The clim ws me in the book n uring clss iscussion tht the mgnetic fiel from loop of current is tht of mgnetic ipole. Verify this clim using objects from your kit. Explin your ie, your metho n your results. E19: Stright wire, Rectngulr Loop. Consier the long stright wire crrying current I from CH 28, #24 shown in Figure of your textbook. The mgnetic flux in the rectngulr loop ue to the µ 0 + B-fiel from the long stright wire ws etermine to be 2Ib ln. 4π 2 ) The current in the long stright wire increses with time such tht I ( t) = I0t + c, where I n c re positive constnts. Assume tht the rectngulr loop hs resistnce R, n tht it 0 is hel fixe long with the long stright wire. Determine the mgnitue of ny current inuce in the rectngulr loop s function of time n ny provie or funmentl constnts. b) The rectngulr loop is relese from rest so tht it is free to move. Determine the irection the of the net force (if ny) cting on the loop fter it is relese. Explin your nswer. c) The rectngulr loop is relese from rest so tht it is free to move. Determine the irection of the torque (if ny) cting on the loop immeitely fter it is relese; tke the center of the loop s the reference point. Explin your nswer.