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# The the center of the loopofb floopb loop at axis

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Unformatted text preview: f if (center pdt circular loops) ﬁeld point. If I. Theare NBloops, L on theS dBx x S S y tract 2a I+ L 2r Eu B = to I (for N loops, multiply r Long cylindrical conductor of radius R Inside SThe magnet’sr 6 R conductor, m0 each Iother) I S I theseP lar to B and 2p R2I x S a plied by N.the the center of the loop,ofB= FloopB loop At axis from the center x the0. (See distance x along m0 NI lation- CHAPTER d (center of N circular loops) B= center of the dBxB I F Atmotion causes a O z N (28.17) 2a expressions by N)x Bx = S r Example 28.6.) to the ﬁeld point. If there are N loops, the ﬁeld is multia u force 2a changing magnetic Binduced I m0S I S I I P xS = 0. field through the 7 (center of N circular loops)E = S B S : 0B2r d l G d£ S R = conductor, r 1v m I (29.7) Bx x uced electric ﬁelds: When plied byis induced center of the loop, Outside(SeeB an emf N. At the by a nth. their d S S Long cylindrical conductor of radius R E B = 2pr S E d l = Inside inducing a r 6 R - oil, conductor, (29.10) tegral S C Example 28.6.) (28.20) B d l = m Iencla stationary conductor, 2p R2 B dt S nging through S tion ofmagnetic ﬂuxlaw: 0Faraday’s law states that the induced emf that cthe line the coil. A S S B C states I cS Sin integral urrentBd £ B Ampere’s law: Ampere’s law et cur- Faraday’s (28.20)a closed loop moves in a S 0 Iencl B=m Long, closely wound of nonelectrostatic Inside Er du B near center A B d l = m(29.3) (all orSpart of 0 nI solenoid, B= re is an induced electric ﬁeld E solenoid S mple B increasing I m I S S in a closed loop unit length, around any the time rate of r Outside the net the near f conductor, r sitive ﬁeld isnnonconservative of B negative of closed path equals m0 times S dt cur-E7 = vBL S B ﬁeld) B = 0 (29.6) R E with turns per equals and cannot be asso-moves in a magnetic ﬁeld, Motional emf: If a conductor r du B S in. This S S dpath. The positive u 2prThe magnet’s B r S S fv rentlaw: through the area enclosed by the E dl change of magnetic ﬂux through the loop. This relation. (See a potential. (See Example 29.11.)Ampere’s law states that the line integral Ampere’s L Outside and S (conductor m0 IS length L movesBin uni-motion causes a du B d l = with (28.20) 0 ed with its midpoint S a motional emf is change is(See Examples 29.9solenoid N encl dl sense induced. S ship is valid whether the ﬂuxsolenoid is caused by a by a right-hand rule. (See A B = m0 nI Long, closelyaround of current path equals m0 times the solenoid, nearform B ﬁeld, L and S both perpendicu-changing mIagnetic = qvB B Inside net curcenterS of B wound any closed determined F r du F = qE v m0 NI 29.10.) ﬁeld,unit S S r+ magnetic motion the field through the f+ the – ent or emf changing withIatoroidalExamples 28.7–28.10.) orelectric ﬁelds: WhenBan emf is induced by a always tends toturns throughlength,out Induced both. path. The positive oppose or cancelofnear loop, Tightly woundn 2rent persolenoid area enclosed by the WithinChange in enclosed by the and to each other...
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## This document was uploaded on 03/13/2014.

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