PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments, ou re fmilir with the concepts of electric nd mgnetic fields. The most importnt formule relted to this topic describe the forces electric nd mgnetic fields exert on electric chrges. In fct, these formule re used to define fields themselves. Electrons crr one unit of negtive elementr chrge. Since n electric or mgnetic field exerts force on electrons, it ffects their motion. In spite of the fct tht electric fields re everwhere round us, in everd life we do not directl observe the motion of electrons. However, such observtions re possible with device clled cthode-r tube (CRT), which is just technicl nme for tube which ws present in erl T sets nd computer monitors, some of which re still in use. PURPOSE Exmine reltionship for electric nd mgnetic forces exerted on moving electric chrges. PRE-LAB ASSIGNMENTS A. Redings: In n electric field E, n electron experiences force F e E where e is the electric chrge of the electron. (1) In mgnetic field B, the electron is subject to force F ev B (2) where v is the velocit of the electron. A force cuses ccelertion ccording to the reltion F m (3) where m is the mss of the electron. Note from (1) nd (2) tht the electric field ccelertes n electron in the direction prllel to the electric field, while the mgnetic field ccelertes n electron in the direction perpendiculr to both the mgnetic field nd the velocit of the electron. P g e 1
Figure 1. Cthode-r tube. A cthode-r tube (Fig. 1) is vcuum tube in which electrons re emitted t one end from hot piece of metl (the cthode) nd then ccelerted b strong electric field creted in the electron gun. The trvel cross the tube, where the re lso subject to being deflected b electric fields creted between two pirs of prllel pltes. Electrons eventull hit the opposite end of the tube. This end is covered with fluorescent mteril, nd serves s screen. Electrons tht strike the screen cuse the fluorescent mteril to glow, nd thus the bem of electrons is visible s spot on the screen. The ctul position of the spot depends on the deflecting field inside the tube. Since electrons in the tube move t high speeds, their motion m be lso ffected b mgnetic fields. B observing the position of the bright spot on the screen, we cn mesure the deflection of electrons b electric nd mgnetic fields. Let us nle the motion of electrons in the tube. The electrons re ccelerted to velocit v in the electron gun. If the ccelerting electric potentil is we cn estimte v from the conservtion of energ, since the increse of the kinetic energ of the electron equls the chnge of potentil energ in the electrosttic field, e. Neglecting the initil speed of the electron, we hve: 1 2 mv 2 e (4) ELECTRIC DEFLECTION The electrons move with the constnt velocit v until the rech the deflecting pltes. Let us ssume tht the deflecting electric field is verticl. If the potentil difference between the pltes is, the electric field in between the pltes is pproximtel uniform nd hs mgnitude of: E (5) d where d is the plte seprtion (see Fig. 2). This electric field will ccelerte electrons in verticl directions with which cn be obtined from formule (1), (3) nd (5): P g e 2
F e E e (6) m m d m Thus, electrons cquire verticl component of velocit v t, where t is the time spent in the deflecting region. If the length of the pltes is l, we cn obtin t from: t l v. Therefore, v e l (7) d mv Figure 2. Deflection of electron bem in the tube. The quntit mesured in the experiment is the verticl bem displcement D on the screen (see Fig. 2). Electrons trvel with constnt velocit between the pltes nd the screen. If t is the time in which electrons trvel from the deflecting pltes to the screen, then D v t. The time t cn be found from t L v, where L is the horiontl distnce from the deflecting pltes to the screen. Combining these two equtions D Lv v, nd using Eq. (7) we obtin 2 D e l L ( d mv ). Since from Eq. (4) 2 e ( mv ) 1 (2 ), we get ll 1 D d2 (8) This formul tells us tht the verticl displcement of the bem should be directl proportionl to the deflection voltge (nd lso to the deflecting electric field E ) nd inversel proportionl to the ccelerting voltge. You will verif this sttement in the experiment. MAGNETIC DEFLECTION The CRT used in the Lb does not contin n electromgnets; therefore, the mgnetic field B will be creted b externl coils. The mgnetic field will be pproximtel uniform, horiontl nd perpendiculr to the electron flight direction. The mgnetic force cting on electrons will be, therefore, directed long the verticl xis F evb (from Eq. (2)). Even though it is not rigorousl correct, we cn ssume tht the mgnetic field cts on electrons long the distnce l nd tht the trvel distnce L to the screen. Thus, v l v F l ( mv ) el B m. Following the sme steps s in the previous section, it cn be shown tht l L D e 1 2 m (9) The verticl displcement of the bem should be directl proportionl to the deflecting B P g e 3
mgnetic field B nd inversel proportionl to the squre root of the ccelerting voltge. Agin, ou will verif this reltion in the experiment. In this experiment, ou will not know B in bsolute units but ou will monitor the vlue of B b mesuring the voltge cross the coils coil. This voltge is directl proportionl to the current in the coils which, in turn, is directl proportionl to the strength of the mgnetic field creted b the coils. LABORATORY ASSIGNMENTS Cution High oltge The cthode-r tube is under voltge of 500, which m be dngerous to our life. Do not touch the connections on the rer end of the cthode-r tube. The power suppl wiring should be done b the instructor. Do not chnge n connection except those to the btter, the 30 power suppl, the voltmeter, the deflecting pltes nd the electromgnet. Mterils Needed: Figure 3. Regulted Power Suppl for the CRT. Cthode-r tube Regulted power suppl for the tube 4.5 Btter 0-30 Power Suppl Experiment A: Electron motion in n electric field smll permnent mgnets (B) Two solenoids (B) Compss Cbles LoggerPro (optionl) P g e 4
Procedures Figure 4. Drwing of experimentl pprtus. A-1. The pprtus should be wired up b our instructor before ou come to the lbortor. You m check connections ginst Fig. 4. Leve the 30 power suppl nd voltmeter off nd disconnected for now. Check tht the 4.5 btter is connected to the sstem (see Fig. 4). Turn the regulted power suppl from the OFF to the STANDBY position nd leve it t this position for one minute. You should see red glow ner the rer end of the cthode-r tube. A-2. Turn the regulted power suppl to the ON position. The totl ccelerting voltge is the sum of two voltges, the C voltge (controlled b the left knob) nd the B+ voltge (controlled b the right knob); see Fig. 3. The voltmeter displing the C or B+ voltge is plced on the left of the power suppl, nd hs two rnges: 0 400 for B+ (the upper scle) nd 0 130 for C (the lower scle). The rnge switch for the meter is t the center of the power suppl. Set this switch to the position on the right. P g e 5
r the B control knob on the power suppl nd observe the voltge chnge on the dul-rnge voltmeter. Set the B+ voltge to pproximtel 350. Set the switch to the position on the left nd using the left knob, vr the C voltge. Set the C voltge to the vlue tht gives mximll shrp spot on the screen (pprox. 125 ). Record the vlue of (i.e. sum of B+ nd C voltges) in the tble in Report Sheet III 1. In the bsence of deflection voltge, the bem spot should be ner the center of the screen. Its position cn be chnged b creful djustment of the position of smll mgnet plced on top of the tube (do not chnge the mgnet s position unless necessr). If ou cnnot get shrp spot, or cnnot get it ner the center, sk the instructor for help. A-3. Connect the 30 power suppl to the verticl deflection pltes. Importnt: The B+ output on the regulted power suppl must be connected (in ddition to its CRT connection) to the negtive output of the 30 power suppl for ll experiments. Filure to mke this connection m result in big increse in the bem spot sie. Leve the horiontl deflection pltes nd the coils unconnected. Connect lso the digitl voltmeter to red the deflection voltge (note tht Fig. 5 shows the voltmeter connected to the coils, which will be the cse in experiment B). Using the knob on the 30 power suppl, vr the deflection voltge nd observe the motion of the bem cross the screen. If the bem moves digonll ou must hve connected both verticl nd horiontl deflection pltes to the power suppl disconnect the horiontl pltes. If the bem moves horiontll swp the 30 power suppl connection to the other deflection plte leds. The spot will move from ero onl in one direction (e.g. in +Y direction). To deflect the spot in the opposite direction (e.g. in Y direction), chnge the polrit of the connection to the 30 power suppl. A-4. In this step, ou will mesure nd plot the displcement D versus the pplied deflection voltge for two different settings of the ccelerting voltge. Becuse the mesurements of the deflecting voltge cn be mde much more precisel thn the position on the screen, ou should mesure the deflection voltges corresponding to few definite positions of the spot, for instnce when the center of the spot crosses the division mrks on the screen. For ech mesurement mke point on the grph included in Report Sheet III 1. Mesure deflective potentil t lest three division mrks down nd t lest three division mrks up of the center. Cover the lrgest rnge of bem deflections llowed b the division mrks nd the voltge rnge. Plot the dt s the re tken without tbulting them, except for the lrgest deflections up ( D ) nd down ( D d ). Record D nd for these extreme deflections in the tble in Report u P g e 6
Sheet III 1 next to the vlue of for this set of mesurements. Reduce the vlue of the voltge B+ b pproximtel 100 nd djust the voltge C to obtin shrp spot. Record the new vlue of. Repet the previous mesurements of D versus the deflection voltge, recording them on the sme grph. Also put coordintes of the lrgest devitions into the tble together with the new vlue of. If the theor discussed bove is correct, ou should obtin two different stright lines, ech corresponding to different vlue of the ccelerting voltge. Clculte the slopes of those lines from the dt in our tble: Slope D D u d u d From Eq. (8) the slope of the dependence of D is equl to l L ( d 2) 1, thus it should be inversel proportionl to. erif this expecttion b clculting the product of nd of the mesured slope (store our result in the 6 th column in the tble). These products should be independent of if Eq. (8) is right. Assuming d 02, L 5, l 1 clculte the slopes predicted b Eq. (8) nd compre them with wht ou ctull mesured (Report Sheet III 1). Experiment B: Electron motion in mgnetic field Procedures Figure 5. Connection of the power suppl to the coils. P g e 7
B-1. The two coils should be positioned nd wired s shown in the Fig. 4. Switch off the 30 power suppl, disconnect it from the deflective pltes nd connect it to the coils. There should still be connection between the B+ output of the regulted power suppl nd the negtive output of the 30 power suppl. Fig 5 shows the simple connection of power suppl to the solenoid coil. Turn the voltge setting to bout 3. You cn red the voltge on the power suppl. Use smll compss to check the direction of the mgnetic field produced b ech coils. Tp the compss since needle cn sometimes get stuck. Mke sure, tht the polrit of the two electromgnets is the sme. You should observe verticl deflection of the spot cused b the mgnetic field. Mesure nd plot, on the grph provided on Report Sheet III 2, the deflection D versus the voltge drop cross the coils (which is proportionl to the mgnetic field). Use the method suggested in A-4 to obtin the dt points. Switch the ~3 power suppl connection to reverse the current flow in the coils. The spot should now be deflected in the opposite direction. Mke mesurements of D versus the voltge drop lso for this configurtion. As in experiment A, chnge the B+ voltge b 100, djust C nd repet the mesurements for the second vlue of the ccelerting voltge. For ech vlue of the ccelerting voltge (sum of B+ nd C voltges) clculte the slope. Store our results in the tble. For the 6 th column in the tble, clculte the product of nd of the mesured slope. These products should be independent of if Eq. (9) is right. Do our results confirm the expected dependence on? B-2. (Absolutel Mndtor) Switch off the power suppl. Disconnect one led from the btter. Reduce the B+ nd C voltges to ero. Switch off the big power suppl. Show our tble to the instructor before turning in our report. P g e 8
REPORT SHEET III 1 Dte Nme Instructor Prtner(s) A-4 Use the grph pper" below to mke grphs displing the displcement D versus the deflection voltge (with the deflection voltge on the x-xis) for the two different vlues of the ccelerting voltge. Optionl: crete our grph in LoggerPro insted. Tr to drw stright line through ech set of our mesurements (use ruler). Is the reltion between D nd liner (circle nswer)? es no Deflection up D u u D d Deflection down Slope Mesured Expected d Slope Slope () (in) () (in) () (in/) (in) (in/) Do our results confirm the expected dependence on (circle nswer)? es no Do the expected slopes roughl gree with the observtions? es no P g e 9
REPORT SHEET III 2 Dte Nme Instructor Prtner(s) B-1 Below mke grph showing D versus the voltge through the coils. Tr to drw stright line through ech set of our mesurements (use ruler). Is the reltion between D nd coil liner (circle nswer)? es no Deflection up Deflection down D u D u d d Mesured Slope Slope () (in) () (in) () (in/) (in ) Do our results roughl confirm the expected dependence on? es no P g e 10
Nme Dte Instructor Exercise 1. PRE LAB EXERCISES Electrons in cthode-r tube re ccelerted long the length of the tube (in the -direction) b potentil difference = 300 olts. Wht is the speed of electrons in m/s when the hit the screen? (c = 3 10 8 m/s; electron mss m = 9.1 10-31 kg cn lso be expressed s m = 5 10 5 eolts/c 2 ). Accelertion of n electron Exercise 2. In ddition to the ccelerting voltge bove, electrons re lso subject to deflection voltge 30. Wht will be the verticl deflection on the screen D, if the deflecting pltes of length l 1 re seprted b distnce d 02, nd the distnce from the pltes to the screen is L 5. Hint: Use Eq. (8). P g e 11