Physics 30 Lesson 20 Magnetic Foces Chaged Paticles I. Chaged paticles in extenal agnetic fields In the pevious lesson we leaned that when a chaged paticle is in otion, a agnetic field is induced aound the paticle which is pependicula to the otion of the paticle. x induced agnetic field aound the paticle positive paticle oving into page What would happen if this paticle was pojected though an existing agnetic field, say between two ba agnets? extenal agnetic field x ba agnet ba agnet The induced agnetic field aound the oving paticle will inteact with the extenal agnetic field, esulting in a foce. The diection of the foce can be deteined by studying how the agnetic fields inteact. In the diaga below, the sybol epesents the diection of the induced agnetic field aound the paticle at that point. The aow head is like an induced noth pole and the tail is like an induced south pole. x esulting net foce ote that above the paticle, the induced agnetic field aow is attacted towad the south and noth poles of the agnets, esulting in a downwad foce. elow the paticle, the induced and extenal agnetic fields epel one anothe, esulting, again, in a downwad foce. The esult of a chaged paticle going though a agnetic field is the paticle will be deflected by a foce which is pependicula to both the oiginal diection of the paticle's otion and the extenal agnetic field. D. Ron Licht 20 1
II. Thid hand ule Diection of the agnetic foce To find the diection of the foce between a paticle and an extenal field, we use the thid hand ule. otice that we ae dealing with thee quantities; paticle diection (v), agnetic field diection () and foce diection (F), which ae all pependicula to each othe. This is siila to the x, y and z coodinates fo atheatics whee x and y ae in the plane of the page and z points pependicula out of the page. Refe to Peason pages 593 to 597. y z x The thid hand ule is: The finges point in the diection of the extenal agnetic field () fo noth to south. The thub points in the diection of the paticle s otion (v). The pal indicates the diection of the esulting foce on the paticle (F). Like the othe hand ules, the ight hand is used fo positive chages and the left hand is used fo negative chages. xaple 1 Fo the following diaga, what is the diection of the deflecting foce if the paticle is: A. an electon. an alpha paticle. x A. Using the left hand (negative chage), the finges point to the ight and the thub points into the page the pal indicates a foce up the page.. Using the ight hand (positive chage), the finges point to the ight and the thub points into the page the pal indicates a foce down the page. D. Ron Licht 20 2
III. Magnitude of the deflecting foce The deflecting foce on a chaged paticle oving though an extenal agnetic field is calculated using: F qvsin whee F q v deflecting foce fo the agnetic field () agnetic flux density o agnetic field stength (Tesla) (T) chage of oving paticle (C) speed of paticle (/s) angle between v and The axiu deflecting foce will occu when v and ae pependicula ( = 90 o ). ince sin 90 o = 1 F qv xaple 2 A 20 g paticle with a chage of +2.0 C entes a 0.020 T agnetic field at 90 o to the field. If the speed of the paticle is 40 /s, what is the acceleation that is expeienced by the paticle in the diaga below? The ight hand ule tells us that the paticle will be deflected upwad out of the page. F qv + 6 F 0.020T(40 )(2.0 10 C) xaple 3 6 F 1.6 10 F a a a T s 6 1.6 10 upout of page -2 2 s 0.000020kg 8.0 10 upout of page What is the agnetic field stength if an electon taveling at 400 /s expeiences a deflecting foce of 2.0 x 10-19 when it entes at 90 o to the field? F qv F qv -19 2.0 x 10 (1.6 x 10-19 C) (400 / s) -3 3.1x 10 T D. Ron Licht 20 3
xaple 4 An alpha paticle entes a 50 T field at 30 o to the field at a speed of 500 /s. What is the deflecting foce expeienced by the alpha paticle? F qv sin F (3.20x10 C)(500 )(0.050T)sin30 F -18 4.0x10-19 s IV. Paticles in agnetic fields When a chaged paticle entes a agnetic field at 90 o to the field, the paticle expeiences a foce which is pependicula to its velocity. Conside the diaga below of a negative paticle enteing a agnetic field. X X X X X X X X F X X X X An 2+ paticle has a chage of 2 x 1.60 x 10-19 C = 3.20 x 10-19 C. X s epesent a agnetic field () acting into the page The esult is that while the speed of the paticle is not effected, the diection of the paticle s otion changes. Recall fo Physics 20 that a foce acting pependicula to the otion of an object esults in unifo cicula otion. Theefoe, the agnetic foce anifests as a centipetal foce: F F c 2 v qv (note that one of the v s cancels out) v q This is a vey ipotant elationship that we will be woking with thoughout the eainde of the couse. Refe to Peason pages 596 to 601 fo a discussion of paticle otion in a agnetic field. xaple 5 X X X X An electon taveling at 6.0 x 10 6 /s entes a agnetic field of 40 T. What is the adius of the electon's path? F F c v qv v q 2-31 6 (9.1110 kg)(6.0 10 s ) -19-3 (1.6 10 C) (40 10 T) ote: Fo pobles involving a paticle enteing a agnetic field the deivation of the elationship between speed, ass, chage, adius of cuvatue and agnetic field stength ust be always be shown. -4 8.54 10 D. Ron Licht 20 4
V. Velocity selectos A velocity selecto is a device fo easuing the speed of a chaged paticle. The dawing shows a velocity selecto that consists of a cylindical tube located within a constant agnetic field. Inside the tube thee is a paallel plate syste that poduces a unifo electic field. A oving chaged paticle, in this case a positive chage, expeiences a agnetic foce and an electic foce at the sae tie. If the agnetic and electic foces ae equal F and opposite, the net foce on the chaged paticle is zeo esulting in the paticle oving undeflected though the fields. The foces ae balanced, F F q qv v ote that only paticles with a paticula speed will pass though the selecto. Fo paticles with diffeent speeds the foces will not be equal and the paticle will be deflected away eithe up o down. xaple 6 ote: Fo pobles involving a velocity selecto, the deivation of the elationship between speed, electic field stength, and agnetic field stength ust be always be shown. An electon entes an electic field (4.5 x 10 5 /C) and a pependicula agnetic field (2.5 x 10-2 T) and passes though both fields undeflected. What is the speed of the electon? F F q qv F v v 5 4.510 /C -2 2.5 10 T 1.8 10 7 s VI. Mass spectoete (ass spectogaph) An instuent that akes use of the cobination of centipetal otion and agnetic deflection of chaged paticles is the ass spectoete. A ass spectoete is an instuent that sepaates paticles accoding to thei asses. ay, fo exaple, a scientist wants to study the isotopes of lithiu. Isotopes, you ay ecall fo cheisty, have the sae atoic nube (nube of potons) but a diffeent atoic ass (nube of potons + neutons). The eleent is fist placed in an ion geneation and acceleato chabe whee it is ionized (the atos ae stipped of thei oute electons) esulting in Li + ions. The ions ae then acceleated though an electic potential and they pass into the spectoete. ince evey ion has the sae chage, speed and initial path, any diffeences in thei cicula paths ae due to diffeences in ass the lighte isotopes will tavel in salle cicles than heavie isotopes. D. Ron Licht 20 5
Mass spectoetes have thee basic pats: 1. ion souce and acceleato 2. a velocity selecto 3. an ion sepaato saple Ion geneation and acceleation chabe 1 + + + + + + + x x x x x x x x x x x x x x x x x x x x x x x x x x x x electified plates 2 ion detecto plate Ion geneato and acceleato Atos ae ionized eithe by extee heating o by electical dischage. The ions ae then acceleated though a potential diffeence (V) whee they gain kinetic enegy qv (see Lesson 16). k Velocity selecto Once the ions pass though the acceleato opening they will have diffeent speeds depending on the chage and ass of the ion. The ion sepaation chabe equies that the ions have the sae speed so they ae passed though a velocity selecto. The velocity selecto is coposed of a unifo agnetic ( 1 ) and an electic field which ae pependicula to each othe. The ion expeiences a agnetic foce in one diection and an electic foce in the opposite diection. If the foces ae balanced, F F q v qv 1 1 only paticles with a cetain speed will pass though the selecto. Fo paticles with diffeent speeds the foces will not be equal and the paticle will be deflected away fo the enty point into the ion sepaato. Ion sepaato Afte leaving the velocity selecto, the chaged paticles ente a diffeent agnetic field ( 2 ) that deflects the ions in a cicula path. F F c velocity selection chabe ass spectoete ion sepaation chabe 2 v qv 2 q 2 v An ion detecto aks the point whee the ion contacts the detecto plate. The adius of the cicula path can then be easued and the ass of the isotope is calculated. D. Ron Licht 20 6
xaple 7 Uaniu isotopes, uaniu 235 and uaniu 239, can be sepaated using a ass spectoete. The uaniu 235 isotope tavels though a salle cicle and can be gatheed at a diffeent point than the uaniu 239. Duing Wold Wa II, the Manhatten poject was attepting to ake an atoic bob. Uaniu 235 is fissionable but it akes up only 0.70% of the uaniu on ath. A lage ass spectoete at Oakidge, Tennessee was used to sepaate uaniu 235 fo the aw uaniu etal. Uaniu 235 and uaniu 239 ions, each with a chage of +2, ae diected into a velocity selecto which has a agnetic field of 0.250 T and an electic field of 1.25 x 10 7 V/ pependicula to each othe. The ions then pass into a agnetic field of 2.00 T. What is the adius of deflection fo each isotope? A chage of +2 eans that each ion has lost two electons. Theefoe q = 2 x +1.60 x 10-19 C = +3.20 x 10-19 C ince each poton and neuton has a ass of 1.67 x 10-27 kg, the ass of each isotope is. 235 = 235 x (1.67 x 10-27 kg) = 3.9245 x 10-25 kg 239 = 239 x (1.67 x 10-27 kg) = 3.9913 x 10-25 kg Fo the velocity selecto: F F q qv 1 1.25 10 v 5.00 10 0.250T 1 Fo the ion sepaato F F uaniu 235 7 V 7 s -25 7 (3.924510 kg)(5.00 10 s ) 235-19 -3 c v qv v q (3.20 10 C) (2.00 10 T) 4 235 3.07 10 2 uaniu 239-25 7 (3.991310 kg)(5.00 10 s ) 239-19 -3 (3.20 10 C) (2.00 10 T) 4 239 3.12 10 D. Ron Licht 20 7
VII. Van Allen adiation belts When a chaged paticle entes a lage agnetic field at an angle between 0 o and 90 o, the paticle will begin to spial towad one of the agnetic poles. The spial esults fo pat of the paticle's velocity being conveted into cicula otion and the eainde keeps the paticle oving along a path pependicula to the otation of the cicula coponent. The ath has a lage agnetic field suounding it. Incoing chaged paticles fo the sun inteact with the agnetic field and spial towad eithe the noth o south pole. When they eventually ente the ath's atosphee, the collisions between the paticles and the atospheic gases ceate the Auoa oealis (nothen lights) and the Auoa Austalis (southen lights). If the agnetic field was not thee, the chaged paticles ay each the ath's suface and ay be haful to life. In 1958, a tea of scientists finally confied the existence of the spialing paticles. The agnetic field aea containing the chaged paticles is now called the Van Allen Radiation elt in hono of the scientist leading the tea. VIII. lack and white television ince a agnetic field changes the path of a oving electon, a popely designed field can diect an electon wheeve the designe wishes. In a television pictue tube, electons ae fied though a potential diffeence of about 50000 V and ae then diected by hoizontal and vetical agnetic coils towad the font of the pictue tube the TV sceen. The sceen is coated with a thin fil of phosphous ateial. When an electon hits the coating, the coating glows fo a bief instant. Thus, if the electons ae popely diected, a pictue can be foed. agnetic coils phosphoou s sceen electon gun An iage on the TV sceen is actually a seies of still pictues seen in apid sequence. As in otion pictues, the ipession of otion is only an illusion. ut in TV, you do not see one coplete pictue at one tie. ach pictue on the sceen (thee ae 30 coplete pictues being scanned evey second) is sketched by a oving spot of vaying intensity. The spot is poduced as the electons stike the coating and poduce visible light. To poduce a single coplete pictue, the spot taces 525 lines. This eans that the electon bea akes 15750 hoizontal passes evey second. The electon bea ust be contolled with geat speed and pecision. D. Ron Licht 20 8
IX. Pactice pobles 1. Fo the following diaga, what is the diection of the deflecting foce if the paticle is: A. a poton.. a fluoide ion. x 2. Tace out the path of the positive paticle in the indicated agnetic field. 3. What is the agnetic field stength if a deflecting foce of 0.0010 is poduced on a 7.5 C paticle enteing the field at 30 o with a speed of 30 /s? (8.89 T) D. Ron Licht 20 9
X. Hand-in assignent 1. What is the diffeence between a peanent agnet and an electoagnet? 2. The poles of a hoseshoe agnet ae aanged so that the oth Pole is diectly ove the outh Pole. A negatively chaged object passes between the poles fo left to ight. What is the diection of the esulting foce? (Daw a diaga.) 3. Thee paticles ove though a constant agnetic field and follow the paths shown in the dawing. Deteine whethe each paticle is positive, negative o neutal. Give easons fo you answes. 4. Thee paticles have identical chages and asses. They ente a constant agnetic field and follow the paths shown in the pictue. Which paticle is oving fastest, which is oving slowest? Justify you answe. 5. The dawing shows a top view of fou inteconnected chabes. A negative chage is fied into chabe 1. y tuning on sepaate agnetic fields in each chabe, the chage can be ade to exit chabe 4. (a) Descibe how the agnetic field in each chabe should be diected. (b) If the speed of the paticle is v when it entes chabe 1, what is its speed when it exits chabe 4? xplain. D. Ron Licht 20 10
6. What deflecting foce is exeted on a chage of 40 C oving at 15 c/s at 30 o to the agnetic field whose flux density is 0.025T? (7.5 x 10-8 ) 7. What happens to the otion of an electon that is oving in the sae diection as (i.e. paallel to) the agnetic field which it entes? 8. What is the deflecting foce on an alpha paticle oving at 1.0% of the speed of light diectly acoss a agnetic field whose flux density is 0.0030 T? (2.9 x 10-15 ) 9. An electon and a poton, each with a speed of 1.2 x 10 2 /s ente a agnetic field of 0.0020 T at 90 o to the field as shown below. A. Calculate the foce on each paticle. (3.84 x 10-20 ). Calculate the acceleation expeienced by each paticle. (4.2 x 10 10 /s 2 out of page, 2.3 x 10 7 /s 2 into page) 10. A agnesiu ion (Mg 2+ ) taveling at 60 000 /s entes a ass spectoete with a agnetic field of 0.0800 T at an angle of 90 o to the field. What is the adius of the cuve followed by the agnesiu ion? (9.39 x 10-2 ) 11. Calculate the agnitude and diection of the agnetic foce on an alpha paticle oving south at a speed of 7.40 x 10 4 /s though a vetically upwad agnetic field of 5.50 T. (1.30 x 10-16 west) 12. The sola wind is a thin hot gas given off by the sun in all diections. oe of the chaged paticles ente the agnetic field of the ath and can expeience a agnetic foce. uppose soe chaged paticles taveling at 9.0 x 10 6 /s encounte the ath's agnetic field at an angle of 90 o whee the agnitude of the field is 1.2 x 10-7 T. Find the adius of the cicula path on which the paticle would ove it wee (a) an electon and (b) a poton. (4.3 x 10 2, 7.8 x 10 5 ) 13. An alpha paticle with a speed of 4.4 x 10 5 /s oves pependicula to a 0.75 T agnetic field in a cicula path with a adius of 0.012. What is the agnitude of the chage on the heliu nucleus? (3.2 x 10-19 C) 14. An ion souce in a paticula ass spectoete poduces deuteons (a deuteon has twice the ass of a poton, but the sae chage). ach deuteon is acceleated fo est though a potential diffeence of 2000 V afte which it entes a 0.600 T agnetic field. Find the adius of the cicula path. (0.0152 ) *15. An electon, taveling at a speed of 3.62 x 10 6 /s, entes a agnetic field with a stength of 0.0373 T at an angle of 75 o to the agnetic field lines. when it entes the agnetic field, the electon has a helix spial (cokscew) path. What is the distance between the spials? (8.73 x 10-4 ) D. Ron Licht 20 11
16. Conside the following diaga that epesents an electon oving into the plane of the page. V = 2000 V between chaged plates d = 0.080 between chaged plates = 0.0028 T The electon entes the electic field, which is pependicula to the agnetic field, and passes though both fields undeflected. The diaga indicates an electon oving into the page. A. Daw vectos on the diaga to indicate the diection of F and F e on the electon.. Calculate the speed of the electon. (8.9 x 10 6 /s) 17. A double chaged unknown ion is shot into a 0.845 T agnetic field between two paallel plates which ae 4.00 apat. When a potential diffeence of 56.8 kv is applied acoss the plates, the paticle passes undeflected though the fields. When the voltage is tuned off, the paticle has a adius of cuvatue of 4.15. A. What is the speed of the paticle? (1.68 x 10 7 /s). What is the ass of the paticle? (6.68 x 10-26 kg) C. Identify the ion. (Ca 2+ ) D. Ron Licht 20 12