March 15. Induction and Inductance Chapter 31

Transcription

1 Mach 15 Inductin and Inductance Chapte 31

2 > Fces due t B fields Lentz fce τ On a mving chage F B On a cuent F il B Cuent caying cil feels a tque = µ B Review > Cuents geneate B field Bit-Savat law = qv B µ 0 ids db = 3 4 π Ampee s s law = B µ = NiA B d s =µ 0 i enc Mach 15, 2004 PHY 184 2

3 > Calculated B field f Lng, staight wie B = µ 0i 2π Cente f lp µ 0i B i = 2R Nte ight-hand ule F the lp Inside slenid (P 1 ) B = µ 0 in n = N / L Mach 15, 2004 PHY 184 3

4 Review > Fce n a wie caying cuent, i 1, due t B f anthe paallel wie with cuent i 2 F = µ Li 2πd > Fce is attactive (epulsive) if cuent in bth wies ae same (ppsite) diectins 0 1 i 2 Mach 15, 2004 PHY 184 4

5 Induced cuents (Fig. 31-1) > A cuent can pduce a B field > Can a B field geneate a cuent? > Mve a ba magnet in and ut f lp f wie Mving magnet twads lp causes cuent in lp Cuent disappeas when magnet stps Mve magnet away fm lp cuent again appeas but in ppsite diectin Faste mtin pduces a geate cuent Mach 15, 2004 PHY 184 5

6 Induced cuents (Fig. 31-2) > Have tw cnducting lps nea each the Clse switch s cuent flws in ne lp, biefly egiste a cuent in the lp Open switch, again biefly egiste cuent in the lp but in ppsite diectin Mach 15, 2004 PHY 184 6

7 Induced cuents (Fig. 31-1) > Cuent pduced in the lp is called induced cuent > The wk dne pe unit chage t pduce the cuent is called an induced emf > Pcess f pducing the cuent and emf is called inductin Mach 15, 2004 PHY 184 7

8 Faaday s s law > Faaday bseved that an induced cuent (and an induced emf) can be geneated in a lp f wie by: Mving a pemanent magnet in ut f the lp Hlding it clse t a cil (slenid) and changing the cuent in the cil Keep the cuent in the cil cnstant but mve the cil elative t the lp Rtate the lp in a steady B field Change the shape f the lp in a B field Mach 15, 2004 PHY 184 8

9 Faaday s s law > Faaday cncluded that an emf and a cuent can be induced in a lp by changing the amunt f magnetic field passing thugh the lp > Need t calculate the amunt f magnetic field thugh the lp s define magnetic flux analgus t electic flux Mach 15, 2004 PHY 184 9

10 Faaday s s law > Magnetic flux thugh aea A Φ B = B da > da is vect f magnitude da that is t the diffeential aea, da > If B is unifm and t A then Φ B = BA > SI unit is the webe,, Wb Wb= T m 2 Mach 15, 2004 PHY

11 Faaday s s law > Faaday s s law f inductin induced emf in lp is equal t the ate at which the magnetic flux changes with time > Minus signs means induced emf tends t ppse the flux change > If magnetic flux is thugh a clsely packed cil f N tuns ε ε dφ = dt B dφ = N dt B Mach 15, 2004 PHY

12 Faaday s s law If B is cnstant within cil Φ B = We can change the magnetic flux thugh a lp ( cil) by Changing magnitude f B field within cil Changing aea f cil, ptin f aea within B field Changing angle between B field and aea f cil (e.g. tating the cil) Mach 15, 2004 B da = BAcsθ ε ε ε ε = N dφ dt PHY B db = NAcsθ dt da = NB csθ dt = d(csθ ) NBA dt

13 Checkpint #1 > Gaph shws magnitude B(t) f unifm B field passing thugh lp, t plane f the lp. Rank the five egins accding t magnitude f emf induced in lp, geatest fist. ε db db = NA csθ = NA b, then d & e tie, then a dt dt & c (ze) Mach 15, 2004 PHY

14 Lenz s s law (Figs. 31-4, 31-5) > Lenz s s law An induced emf gives ise t a cuent whse B field ppses the change in flux that pduced it > As the magnet mves twads, the lp the flux in lp inceases (a),, s the induced cuent sets up B i field in the ppsite diectin (b) (a) (a) ((a)a) Mach 15, 2004 (b) PHY

15 Lenz s s law (Fig. 31-5) > (a) Magnet mves twads lp; the flux in lp inceases s induced cuent sets up B i field in the ppsite diectin t cancel the incease: > B i is in the ppsite diectin t inceasing B > (b) Magnet mves away fm lp; the flux deceases s induced cuent has a B i field in the same diectin t cancel the decease: > B i is in the same diectin as deceasing B Mach 15, 2004 PHY

16 Lenz s s law (Figs. 31-7) Example: electic guita Mach 15, 2004 PHY