Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1

Transcription

1 Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1

2 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs Tribute t New Orleans and Mardi Gras

3 Yur Cmments Hw can a magnetic field pint in a directin? What abut the wire example in the prelecture where is shwn t mve in a cunter-clckwise/clckwise directin? This stuff is really neat... It is fun t actually see the calculatins fr Please explain what causes magnetic fields, and why they exist. Unless we learn that later r nt at all, I just dn t understand. A little at a time! magnetism. Hwever, since this is the first time I ve really seen it, it is still a bit cnfusing. If yu culd g thrugh different examples and g ver the actual cncepts mre, that wuld be great. Magnets. Hw d they wrk? Gd questins! ut very deep! What are we suppsed t d if we have tw left hands? Culd yu g ver this right hand rule again? There are s many f them... RHR cnfused many I refuse t make an attempt at a bad pun. 05 We mst definitely need examples. Als, every time yu pst an awful pun, a puppy dies. Just s yu knw. Physics 1 Lecture 1, Slide 3

4 Key Cncepts: 1) The frce n mving charges due t a magnetic field. ) The crss prduct. Tday s Plan: 1) Review f magnetism ) Review f crss prduct 3) Example prblem 05 Physics 1 Lecture 1, Slide 4

5 Magnetic Observatins ar Magnets N S N S S N N S Cmpass Needles N S Magnetic Charge? N S cut in half N S N S 07 Physics 1 Lecture 1, Slide 5

6 Magnetic Observatins Cmpass needle deflected by electric current Magnetic fields created by electric currents Directin? Right thumb alng I, fingers curl in directin f Magnetic fields exert frces n electric currents (charges in mtin) I V V F F I I I F F I V 1 Physics 1 Lecture 1, Slide 6

7 Magnetic Observatins P P I (ut f the screen) I (int f the screen) Case I The magnetic field at P pints Case II A. Case I: left, Case II: right. Case I: left, Case II: left C. Case I: right, Case II: left D. Case I: right, Case II: right WHY? Directin f : right thumb in directin f I, fingers curl in the directin f Physics 1 Lecture 1, Slide 7

8 Magnetism & Mving Charges All bservatins are explained by tw equatins: F qv Tday d 4 0 I ds r rˆ Next Week 14 Physics 1 Lecture 1, Slide 8

9 Crss Prduct Review Crss Prduct different frm Dt Prduct A is a scalar; A x is a vectr A prprtinal t the cmpnent f parallel t A A x prprtinal t the cmpnent f perpendicular t A Definitin f A x Magnitude: Asinq Directin: perpendicular t plane defined by A and with sense given by right-hand-rule 16 Physics 1 Lecture 1, Slide 9

10 Remembering Directins: The Right Hand Rule F qv F y x qv z 17 Physics 1 Lecture 1, Slide 10

11 Checkpint 1a Three pints are arranged in a unifrm magnetic field. The field pints int the screen. 1) A psitively charged particle is lcated at pint A and is statinary. The directin f the magnetic frce n the particle is: A psitively charged particle is lcated at pint A and is statinary. The directin f the magnetic frce n the particle is A. right. left C. int the screen D. ut f the screen E. zer all are int the screen Right hand rule says its pinting ut f the screen qvx=0 if v=0. 18 Physics 1 Lecture 1, Slide 11

12 Checkpint 1a Three pints are arranged in a unifrm magnetic field. The field pints int the screen. 1) A psitively charged particle is lcated at pint A and is statinary. The directin f the magnetic frce n the particle is: A psitively charged particle is lcated at pint A and is statinary. The directin f the magnetic frce n the particle is A. right. left C. int the screen D. ut f the screen E. zer F qv The particle s velcity is zer. There can be n magnetic frce. 18 Physics 1 Lecture 1, Slide 1

13 Checkpint 1b Three pints are arranged in a unifrm magnetic field. The field pints int the screen. 1) A psitively charged particle is lcated at pint A and is statinary. The directin f the magnetic frce n the particle is: The psitive charge mves frm A tward. The directin f the magnetic frce n the particle is A. right. left C. int the screen D. ut f the screen E. zer it shuld be diagnally utward v is up, b is int screen, right hand rule says it shuld be left. ecause the magnetic frce ges int the screen, s will the directin 1 Physics 1 Lecture 1, Slide 13

14 Checkpint 1b Three pints are arranged in a unifrm magnetic field. The field pints int the screen. 1) A psitively charged particle is lcated at pint A and is statinary. The directin f the magnetic frce n the particle is: The psitive charge mves frm A tward. The directin f the magnetic frce n the particle is A. right. left C. int the screen D. ut f the screen E. zer F qv qv F X 1 Physics 1 Lecture 1, Slide 14

15 Crss Prduct Practice prtns (psitive charge) cming ut f screen (+z directin) Magnetic field pinting dwn F qv What is directin f frce n POSITIVE charge? A) Left ) Right C) UP D) Dwn E) Zer - x + x + y - y y x 4 z Physics 1 Lecture 1, Slide 15

16 Mtin f Charge q in Unifrm Field Frce is perpendicular t v Speed des nt change Unifrm Circular Mtin Slve fr R: F qv F qv a v R v mv qv m R R q x x x x x R x x x x x x F x q v q x x x x x x x x v x x x x x x x x x x x x x x x v F F q x x x x x x x Unifrm int page F v q 30 Physics 1 Lecture 1, Slide 16

17 mv p R q q LHC 17 miles diameter Physics 1 Lecture 1, Slide 17

18 Checkpint a The drawing belw shws the tp view f tw intercnnected chambers. Each chamber has a unique magnetic field. A psitively charged particle is fired int chamber 1, and bserved t fllw the dashed path shwn in the figure. What is the directin f the magnetic field in chamber 1? A. up. dwn C. int the page D. ut f the page Since the directin f the magnetic field has t be perpendicular t the charged particle s directin, it will pint up.. Having a magnetic field ging int the screen indicates cunterclckwise mtin. 34 Thumb pints t the left because particle is deflected t the left and fingers pint up because that is velcity vectr. Fingers curl ut f the screen. Physics 1 Lecture 1, Slide 18

19 Checkpint a The drawing belw shws the tp view f tw intercnnected chambers. Each chamber has a unique magnetic field. A psitively charged particle is fired int chamber 1, and bserved t fllw the dashed path shwn in the figure. What is the directin f the magnetic field in chamber 1? A. up. dwn C. int the page D. ut f the page F qv qv. F 34 Physics 1 Lecture 1, Slide 19

20 Checkpint b The drawing belw shws the tp view f tw intercnnected chambers. Each chamber has a unique magnetic field. A psitively charged particle is fired int chamber 1, and bserved t fllw the dashed path shwn in the figure. Cmpare the magnitude f the magnetic field in chamber 1 t the magnitude f the magnetic field in chamber A. 1 >. 1 = C. 1 < because the curve is much sharper inside bx 1 It equals ut. ecause the particle changed directin mre slwly in the secnd chamber. 36 Physics 1 Lecture 1, Slide 0

21 Checkpint b The drawing belw shws the tp view f tw intercnnected chambers. Each chamber has a unique magnetic field. A psitively charged particle is fired int chamber 1, and bserved t fllw the dashed path shwn in the figure. Cmpare the magnitude f the magnetic field in chamber 1 t the magnitude f the magnetic field in chamber A. 1 >. 1 = C. 1 < Observatin: R > R 1 mv R 1 q 36 Physics 1 Lecture 1, Slide 1

22 Calculatin A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? q,m E d enters here x 0 / exits here x 0 Cnceptual Analysis What d we need t knw t slve this prblem? (A) Lrentz Frce Law () E field definitin (C) V definitin ( F qv qe) (D) Cnservatin f Energy/Newtn s Laws (E) All f the abve Abslutely! We need t use the definitins f V and E and either cnservatin f energy r Newtn s Laws t understand the mtin f the particle befre it enters the field. We need t use the Lrentz Frce Law (and Newtn s Laws) t determine what happens in the magnetic field. Physics 1 Lecture 1, Slide

23 Calculatin A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? q,m E d enters here x 0 / exits here x 0 Strategic Analysis Calculate v, the velcity f the particle as it enters the magnetic field Use Lrentz Frce equatin t determine the path in the field as a functin f Apply the entrance-exit infrmatin t determine Let s D It!! Physics 1 Lecture 1, Slide 3

24 Calculatin A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? q,m E d enters here x 0 / exits here x 0 What is v 0, the speed f the particle as it enters the magnetic field? qed qe v v ad v v m md (A) () (C) (D) (E) E v m qed m Why?? Cnservatin f Energy Initial: Energy = U = qv = qed Final: Energy = KE = ½ mv 0 Newtn s Laws a = F/m = qe/m v 0 = ad 1 mv qed qe v qed d v m m qed v m Physics 1 Lecture 1, Slide 4

25 Calculatin A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? qed v m q,m d enters here x 0 / exits here What is the path f the particle as it mves thrugh the magnetic field? E x 0 (A) () (C) Why?? Path is circle! Frce is perpendicular t the velcity Frce prduces centripetal acceleratin Particle mves with unifrm circular mtin Physics 1 Lecture 1, Slide 5

26 Calculatin A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? What is the radius f path f particle? R Why?? x qed v m R x 1 R x q,m d enters here x 0 / (A) () (C) (D) (E) R mv q E v R a exits here x 0 R x / Physics 1 Lecture 1, Slide 6

27 Calculatin A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? qed v m R 1 x 0 q,m E d enters here x 0 / exits here x 0 x med q E v E m qed med q (A) () (C) (D) (E) 1 x mv qx Why?? F ma qv m v R m q v R m q x qed m x med q Physics 1 Lecture 1, Slide 7

28 Fllw-Up A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? x med q x 0 / exits here q,m E d x 0 enters here Suppse the charge f the particle is dubled (Q = q),while keeping the mass cnstant. Hw des the path f the particle change? 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 X X X (A) () (C) N slam dunk.. As Expected! Several things ging n here 1. q changes v changes. q & v change F changes 3. v & F change R changes Physics 1 Lecture 1, Slide 8

29 Fllw-Up A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? x med q x 0 / exits here q,m E d x 0 enters here Suppse the charge f the particle is dubled (Q = q),while keeping the mass cnstant. Hw des the path f the particle change? Hw des v, the new velcity at the entrance, cmpare t the riginal velcity v 0? v (A) v () v (C) v v (D) v v (E) v Why?? v v 1 1 mv QEd qed mv v v v v Physics 1 Lecture 1, Slide 9

30 Fllw-Up A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? x med q x 0 / exits here q,m E d x 0 enters here Suppse the charge f the particle is dubled (Q = q),while keeping the mass cnstant. Hw des the path f the particle change? v v Hw des F, the magnitude f the new frce at the entrance, cmpare t F 0, the magnitude f the riginal frce? (A) F F () F F (C) F F (D) F F (E) Why?? F Qv q v F F F F Physics 1 Lecture 1, Slide 30

31 Fllw-Up A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? x med q x 0 / exits here q,m E d x 0 enters here Suppse the charge f the particle is dubled (Q = q),while keeping the mass cnstant. Hw des the path f the particle change? Hw des R, the radius f curvature f the path, cmpare t R 0, the radius f curvature f the riginal path? R Why?? R v v F F (A) R () R (C) R R (D) R R (E) v F m R v R m F v R m F m v F R R R Physics 1 Lecture 1, Slide 31

32 Fllw-Up A particle f charge q and mass m is accelerated frm rest by an electric field E thrugh a distance d and enters and exits a regin cntaining a cnstant magnetic field at the pints shwn. Assume q,m,e,d, and x 0 are knwn. What is? x med q x 0 / exits here q,m E d x 0 enters here Suppse the charge f the particle is dubled (Q = q),while keeping the mass cnstant. Hw des the path f the particle change? 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 X X X (A) () (C) R R A Check: (Exercise fr Student) Given ur result fr (abve), can yu shw: R 1 med Q R R Physics 1 Lecture 1, Slide 3