Electromagnetic Induction

Transcription

1 lectromagnetic Induction

2 Induced MF We already know that moving charge (=current) causes magnetic field It also works the other way around: changing magnetic field (e.g. moving permanent magnet) causes current it s called induced current since there is a current, there is electromotive force called induced emf lectromagnetic Induction

3 Induction xperiments Stationary permanent magnet does not induce current, the moving one does Stationary current in the first coil does not induce the current in the second coil, moving the coil in and out or switching the current on and off does What matters is change of magnetic field lectromagnetic Induction 3

4 Magnetic Flux B A A is like a vector: you need to pick one of the two possible directions BA if B is not perpendicular to surface then B cos B cos A A if Bcosϕ is the same everywhere then BAcos lectromagnetic Induction 4

5 Faraday s aw t rate of flux change for a coil of N turns, N t induced emf [Φ] = weber, 1 Wb = 1 T m =1 V s notice the sign in the formula lectromagnetic Induction 5

6 A Slide-Wire Generator B const B v A vt BA vt t Bv lectromagnetic Induction 6

7 enz s aw The direction of induced current is such as to oppose the direction of the phenomenon causing it enz s law is a particular case of e Chatelier's principle: in a stable equilibrium, any deviation would cause a force which drives the system back to the equilibrium (that s why it s stable!) lectromagnetic Induction 7

8 enz s aw and a Slide-Wire rod I induced current F v B B induced induced field is directed opposite to B direction of induced current is such that force F acting on it due to B tries to slow down the moving rod otherwise we would get infinite acceleration without external force lectromagnetic Induction 8

9 Motional lectromotive Force I v B separate from wires (no current) a F B qvb F q b charges keep accumulating until electric force compensates the magnetic force V ab vb vb lectromagnetic Induction 9

10 Generator =device which converts mechanical energy to electricity t AB t cos t AB sin t need calculus to derive it lectromagnetic Induction 10

11 Alternating and Same Sign emf brush slip ring brush commutator lectromagnetic Induction 11

12 Mutual Inductance =coupling between two coils when current through the main coil changes, the secondary coil gets induced emf the question is, how large is it? N t Φ is proportional to the current in the main coil: 1 M i 1 N 1 for convenience i M 1 1 t lectromagnetic Induction 1

13 Mutual Inductance i M 1 1 t 1 i M 1 t it turns out that M M 1 M 1 even for different coils [M]= henry, 1 H = 1 Wb/A=1 V s/a=1 Ω s mutual inductance M depends on coils geometry and magnetic properties of the material lectromagnetic Induction 13

14 Transformers =two coils that share magnetic flux 1 N 1 t N t 1 N N 1 lectromagnetic Induction 14

15 Self-Inductance =mutual inductance applied to the main coil itself i t Capacitors vs inductors: Inductor: DC: i=0 (R= ) v i C t DC: v=0 (R=0) i v t lectromagnetic Induction 15

16 Magnetic Field nergy Power supplied during time Δt: v i P vi i i t t U Pt ii U 1 I i i lectromagnetic Induction 16

17 Capacitors vs Inductors nergy nergy density Mechanical analog U u CV 0 spring (potential energy) U u I B lectromagnetic Induction 17 0 mass (kinetic energy)

18 Resistance-Inductance Circuits S I 0 R V V ab bc 0 a b c I lectromagnetic Induction 18

19 Resistance-Inductance Circuits lectromagnetic Induction 19 S R a b c I t i ir Switch closed ) ( 0 t t i V i initial ab 0 0

20 Resistance-Inductance Circuits i ir Switch closed ( t 0) t i 0 R S a b c I V ab i t R lectromagnetic Induction 0 0 current increases current change rate decreases i

21 Resistance-Inductance Circuits i ir Switch closed ( t ) t R S a b c I i i t final final R lectromagnetic Induction 1 0

22 Current vs Time i i (1 e tr/ ) need calculus to derive it R i final i final ( 11/ e) /R = time constant e.7188 R t Current, Resistance, and Direct-Current Circuits

23 Current Decay in R Circuit S i i 0 e tr/ i R i 0 a b c I R t lectromagnetic Induction 3

24 The -C Circuit total CV I 1 C C a b c I lectromagnetic Induction 4