Physics 212. Faraday s Law

Transcription

1 Phsics 1 Lecture 17 Frd s Lw Phsics 1 Lecture 17, Slide 1

2 Motionl EMF Chnge Are of loop Chnge mgnetic field through loop Chnge orienttion of loop reltive to In ech cse the flu of the mgnetic field through the circuit chnges with time nd n EMF is produced. da d EMF Phsics 1 Lecture 17, Slide

3 Rotte the loop,chnge flu, generte emf. Phsics 1 Lecture 17, Slide 3

4 Move loop to plce wherethe field is different, chnge flu, generte emf. 1 v Phsics 1 Lecture 17, Slide 4

5 Checkpoint 1 A copper loop is plced in uniform mgnetic field s shown. You re looking from the right. Suppose the loop is moving to the right. The current induced in the loop is: A. zero. clockwise C. counterclockwise Motionl emf is ZERO v X = 0 no chrge seprtion no E field no emf The flu is NOT chnging does not chnge the re does not chnge the orienttion of nd A does not chnge Phsics 1 Lecture 17, Slide 5

6 Checkpoint 1c Now suppose tht the loop is spun round verticl is s shown, nd tht it mkes one complete revolution ever second. The current induced in the loop: A. Is zero. Chnges direction once per second C. Chnges direction twice per second Current chnges direction ever time the loop becomes perpendiculr with the field emf ~ d/ ( da = m) d/ ( da ) = 0 X O da X O da Phsics 1 Lecture 17, Slide 6

7 Frd s Discover emf d True no mtter how we chnge the flu. In fct, the circuit m be sttionr (no motionl EMF) nd onl the -field chnges with time. An EMF is still produced. This implies tht: emf E dl d Frd s Lw

8 Chnge the field in time so flu chnges. Induce n emf nnd therefore n Electric field. This emf tries to oppose the chnge in flu. (Lenz s Lw) emf E d d (t) decresing Induces n E field even if there is no circuit there! Phsics 1 Lecture 17, Slide 8

9 Checkpoint 1b A copper loop is plced in uniform mgnetic field s shown. You re looking from the right. Motionl emf is ZERO Circuit is sttionr! Checkpoint 1b Now suppose the tht loop is sttionr nd tht the mgnetic field is decresing in time. The current induced in the loop is: A. zero. clockwise C. counterclockwise HOWEVER: The flu is chnging decreses in time current induced to oppose the flu chnge clockwise current tries to restore tht ws removed Looking from right 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 X X X X X X X X X Clockwise current tries to restore Phsics 1 Lecture 17, Slide 9

10 Checkpoint A horizontl copper ring is dropped from rest directl bove the north pole of permnent mgnet F O X (copper is not ferromgnetic) Will the ccelertion of the flling ring in the presence of the mgnet be n different thn it would hve been under the influence of just grvit (i.e. g)? A. > g. = g C. < g Like poles repel F totl < mg < g This one is hrd! field increses upwrd s loop flls Clockwise current (viewed from top) is induced Phsics 1 Lecture 17, Slide 10

11 Checkpoint A horizontl copper ring is dropped from rest directl bove the north pole of permnent mgnet HOW IT WORKS Looking down (copper is not ferromgnetic) I I Will the ccelertion of the flling ring in the presence of the mgnet be n different thn it would hve been under the influence of just grvit (i.e. g)? A. > g. = g C. < g This one is hrd! field increses upwrd s loop flls Clockwise current (viewed from top) is induced Min Field produces horizontl forces Fringe Field produces verticl force IL X points UP F totl < mg < g Phsics 1 Lecture 17, Slide 11

12 Clcultion A rectngulr loop (height =, length = b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. b Wht is the direction nd the mgnitude of the force on the loop when hlf of it is in the field? Conceptul Anlsis Once loop enters field region, flu will be chnging in time Frd s Lw then ss emf will be induced Strtegic Anlsis Find the emf Find the current in the loop Find the force on the current Phsics 1 Lecture 17, Slide 1

13 Clcultion A rectngulr loop (height =, length = b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. emf d b Wht is the mgnitude of the emf induced in the loop just fter it enters the field? (A) e = b () e = ½ (C) e = ½ b (D) e = (E) e = b b In time it moves b The re in field chnges b da = Chnge in Flu = d = da = d v o Phsics 1 Lecture 17, Slide 13

14 Clcultion A rectngulr loop (height =, length = b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. d emf b Wht is the direction of the current induced in the loop just fter it enters the field? (A) clockwise () counterclockwise (C) no current is induced emf is induced in direction to oppose the chnge in flu tht produced it b Flu is incresing into the screen Induced emf produces flu out of screen Phsics 1 Lecture 17, Slide 14

15 Clcultion A rectngulr loop (height =, length = b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. Wht is the direction of the net force on the loop just fter it enters the field? emf d b (A) + () - (C) + (D) - b Force on current in mgnetic field: F IL I Force on top nd bottom segments cncel (red rrows) Force on right segment is directed in direction. Phsics 1 Lecture 17, Slide 15

16 Clcultion A rectngulr loop (height =, length = b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. Wht is the mgnitude of the net force on the loop just fter it enters the field? F IL emf d b e = (A) F 4v R () F v R (C) F vo / R (D) o o F vo / R F IL F IL since L b F I I e R v R o F v R o v R o IL Phsics 1 Lecture 17, Slide 16

17 Follow-Up A rectngulr loop (sides =,b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. Wht is the velocit of the loop when hlf of it is in the field? b t = : e = Which of these plots best represents the velocit s function of time s the loop moves form entering the field to hlfw through? (A) () (C) D) (E) X X X This is not obvious, but we know v must decrese Wh? b F right I F right points to left Accelertion negtive Speed must decrese Phsics 1 Lecture 17, Slide 17

18 F v / R m Follow-Up A rectngulr loop (sides =,b, resistnce = R, mss = m) costs with constnt velocit in + direction s shown. At t =0, the loop enters region of constnt mgnetic field directed in the z direction. Wht is the velocit of the loop when hlf of it is in the field? Which of these plots best represents the velocit s function of time s the loop moves form entering the field to hlfw through? (A) (D) dv Wh (D), not (A)? b e = F is not constnt, depends on v F R v dv m v v o e where t mr Chllenge: Look t energ Clim: The decrese in kinetic energ of loop is equl to the energ dissipted s het in the resistor. Cn ou verif?? Phsics 1 Lecture 17, Slide 18