Electrcty and Magnetsm Revew Faraday s Law Lana Sherdan De Anza College Dec 3, 2015
Overvew Faraday s law Lenz s law magnetc feld from a movng charge Gauss s law
Remnder: (30.18) Magnetc Flux feld S that makes an case s (30.19), then u 5 908 and the he plane as n Fgure axmum value). weber (Wb); 1 Wb 5 Magnetc flux plane s a agnetc to the plane. Defnton of magnetc flux S u S d A Fgure 30.19 The magnetc flux through an area element da s S? d S A 5 da cos u, where d S A s a vector perpendcular to the surface. The magnetc flux of a magnetc feld through a surface A s Φ = ( A) da S Unts: Tm 2 If the surface s a flat plane and s unform, that just reduces to: Φ = A
a magnet s moved When the magnet s a loop of wre When the magnet s held moved away from the cted Changng to a senstve flux andstatonary, emf there s no loop, the ammeter sh ter, the ammeter nduced current n the that the nduced curr that a current When as magnet s atloop, rest even nearwhen a loop the of wre there s no s opposte potental that shown d n the dfference loop. across the magnet ends ofs the nsde wre. the loop. part a. I N S N S I N S b c
toward a loop of wre When the magnet s connected to a senstve statonary, there s no ammeter, the ammeter nduced current n th When the north pole of shows the that magnet a current s moved s towards the loop, loop, even the when the magnetc flux ncreases. nduced n the loop. magnet s nsde the Changng flux and emf 1 A smple experment t a current s nduced en a magnet s moved way from the loop. I N a A current flows clockwse n the loop. S b N S
he magnet s held moved away from the ry, Changng there s no flux andloop, emf the ammeter shows current n the that the nduced current en when When the the north pole of s opposte the magnet that shown s moved n away from the loop, s nsde the the magnetc loop. flux decreases. part a. I N S N S c A current flows counterclockwse n the loop.
Faraday s Law Faraday s Law If a conductng loop experences a changng magnetc flux through the area of the loop, an emf E F s nduced n the loop that s drectly proportonal to the rate of change of the flux, Φ wth tme. Faraday s Law for a conductng loop: E = Φ t
Faraday s Law Faraday s Law for a col of N turns: E F = N Φ t f Φ s the flux through a sngle loop.
Changng Magnetc Flux The magnetc flux mght change for any of several reasons: the magntude of can change wth tme, the area A enclosed by the loop can change wth tme, or the angle θ between the feld and the normal to the loop can change wth tme.
Lenz s Law S The magnet's moton creates a magnetc dpole that opposes the moton. Addtonal examples, vdeo, and practce avalable at Lenz s Law 30-4 Lenz s Law An nduced current has a drecton such that the magnetc feldsoon dueafter to the Faraday current proposed opposes hs the law of nduc devsed a rule for determnng the drecton of an change n the magnetc flux that nduces the current. An nduced current has a drecton such that the ma opposes the change n the magnetc flux that nduces t Furthermore, the drecton of an nduced emf s th a feel for Lenz s law,let us apply t n two dfferent where the north pole of a magnet s beng moved to N ascally, Lenz s 1. Opposton law let s us to Pole nterpret Movement. the mnus The approach N Fg. 30-4 ncreases the magnetc flux through µ sgn n the equaton we wrte to represent current n the loop. From Fg. 29-21, we know t Faraday s Law. netc dpole wth a south pole and a north po moment : s drected from south to north. ncrease E = beng Φ caused by the approachng mag thus : ) must t face toward the approachng no S 30-4). Then the curled straght rght-hand rul Fg. 30-4 Lenz s law at work.as the the current nduced n the loop must be counte magnet s 1 moved toward the loop, a current Fgure from Hallday, Resnck, Walker, 9th If we ed. next pull the magnet away from th
: nd 30-5b.Thus, and are now n the same drecton. : In Fgs. 30-5c and d, the south pole of the magnet ap- Law: and retreats Page from the loop, 795 respectvely. n Lenz sproaches Textbook (a) (b) (c) Increasng the external feld nduces a current wth a feld nd that opposes the change. Decreasng the external feld nduces a current wth a feld nd that opposes the change. Increasng the external feld nduces a current wth a feld nd that opposes the change. Decreasng the external feld nduces a current wth a feld nd that opposes the change. A The nduced current creates ths feld, tryng to offset the change. nd nd nd nd The fngers are n the current's drecton; the thumb s n the nduced feld's drecton. nd nd nd nd nd nd nd nd (a) (b) (c) (d) :
unform magnetc feld that exsts Faraday s Law Queston throughout a conductng loop,wth the drecton of the feld perpendcular to the plane of the loop. Rank the fve regons of the graph accordng to the magntude of the emf nduced n the loop, greatest frst. The graph gves the magntude (t) of a unform magnetc feld that exsts throughout a conductng loop, wth the drecton of the feld perpendcular to the plane of the loop. Rank the fve regons of the graph accordng to the magntude of the emf nduced n the loop, greatest frst. a b c d e t
Faraday s Law 30-4 LENZ S LAW 795 nward, The fgure CHECKPOINT shows three stuatons 2 rease n n whch dentcal crcular : conductng The fgure loops shows are three n unform stuatons magnetc n whch felds dentcal that crcular are ether conductng (Inc) loops or are decreasng unform (Dec) magnetc n magntude felds that are at dentcal ether n- nd dhen the creasng (Inc) or decreasng (Dec) n magntude at dentcal ncreasng ard flux rates. In each, the dashed lne concdes wth dameter. Rank the rates.in each,the dashed lne concdes wth a dameter.rank g. 29-21 stuatons the stuatons accordng accordng to the magntude to the magntude of the current of the current nduced n-duced greatest n the frst. loops, greatest frst. the a. loops, ses the an that e magom the but t s ard nn Fg. Inc Inc Inc Dec Dec Inc net ap- (a) (b) (c)
Magnetc felds from movng charges and currents We are now movng nto chapter 29. Anythng wth a magnet moment creates a magnetc feld. Ths s a logcal consequence of Newton s thrd law.
Magnetc felds from movng charges A movng charge wll nteract wth other magnetc poles. Ths s because t has a magnetc feld of ts own. The feld for a movng charge s gven by the ot-savart Law: = µ 0 q v ˆr 4π r 2
Magnetc felds from movng charges = µ 0 q v ˆr 4π r 2 1 Fgure from rakeshkapoor.us.
Magnetc felds from currents = µ 0 q v ˆr 4π r 2 We can deduce from ths what the magnetc feld do to the current n a small pece of wre s. Current s made up of movng charges! q v = q s t = q s = I s t We can replace q v n the equaton above.
Magnetc felds from currents Ths element of current creates a magnetc feld at P, nto the page. current-length element a dfferental magnetc nt P. The green (the ) at the dot for pont P d : s drected nto the ds θ ds ˆ r r P Current dstrbuton d(nto page) Ths s another verson of the ot-savart Law: seg = µ 0 I s ˆr 4π r 2 where seg s the magnetc feld from a small segment of wre, of length s.
mmaton Magnetc felds from currents The magnetc feld vector ecause of at any pont s tangent to s a scalar, Magnetc feld a crcle. around a wre segment, vewed end-on: beng the Wre wth current nto the page a current- (29-1) hat ponts constant, (29-2) the cross Fg. 29-2 The magnetc feld lnes produced by a current n a long straght wre
Magnetc felds from currents NETIC How FIELDS to determne DUE TO the CURRENTS drecton of the feld lnes (rght-hand rule): s the da curg. 29-2, ld : at erpend dn of the ) If the o the ed rahe page, (a) (b) Here s a smple rght-hand rule for fndng the drecton of the mag set up by a current-length element, such as a secton of a long wre: The thumb s current's dre The fngers re the feld vecto drecton, wh tangent to a c Rght-hand rule: Grasp the element n your rght hand wth your extended th
Magnetc feld from a long straght wre The ot-savart Law, seg = µ 0 I s ˆr 4π r 2 mples what the magnetc feld s at a perpendcular dstance R from an nfntely long straght wre: = µ 0I 2πR (The proof requres some calculus.)
Gauss s Law for Magnetc Felds Gauss s Law for magnetc felds.: da = 0 Where the ntegral s taken over a closed surface A. (Ths s lke a sum over the flux through many small areas.) We can nterpret t as an asserton that magnetc monopoles do not exst. The magnetc feld has no sources or snks.
Gauss s Law for Magnetc Felds 32-3 INDUCED MAGNETIC FIELDS da = 0 863 PART 3 re complcated than does not enclose the Fg. 32-4 encloses no x through t s zero. nly the north pole of l S. However, a south ce because magnetc lke one pece of the encloses a magnetc Surface II N Surface I S tom faces and curved of the unform and and are arbtrary of the magnetc flux
ates level of problem dffculty Gauss s Law for Magnetsm Queston, Ch32 # 2 n avalable n The Flyng Crcus of Physcs and at flyngcrcusofphyscs.com The fgure shows a closed surface. Along the flat top face, whch has a radus of 2.0 cm, a perpendcular magnetc feld of for Magnetc Felds page. The total elect magntude 0.30 T s drected outward. Along the flat bottom face, rough a magnetc each of fve flux of faces 0.70 of mwb a de s drected (sngular outward. gven Whatby are the E (3.00 N(a) Wb, magntude where and N ( 1 to 5) s the num- onds. What s the m The flux (b) drecton s postve (nward (outward) or for ofn the even magnetcfeld flux through that s the nduced r N odd.what curved parts ofthe flux surface? through the sxth cm and (b) 5.00 cm? closed surface. Along as a radus of 2.0 cm, a feld : of magntude rd. Along the flat botx of 0.70 mwb s dre the (a) magntude d or outward) of the he curved part of the ILW 8 Nonunfor 29 shows a crcular cm n whch an elec the plane of the pa concentrc crcle of (0.600 V m/s)(r/r)t magntude of the nd cm and (b) 5.00 cm? 9 Interactve soluton s at Unform ele
Summary Faraday s law Lenz s law magnetc feld from a movng charge Guass s law Homework Study!