Faraday s Law of Induction Motional emf

Transcription

1 Faraday s Law of Induction Motional emf Motors and Generators Lenz s Law Eddy Currents

2 Te needle deflects momentarily wen te switc is closed A current flows troug te loop wen a magnet is moved near it, witout any batteries!

3 Te emf induced in a circuit is directly proportional to te time rate of cange of te magnetic flux troug te circuit. E were, d da. For N loops, E N d

4 d d E E Acos To induce an emf we can cange, te magnitude of te area enclosed by te loop te angle between and te normal to te area any combination of te above over time.

5 Te permanent magnet inside te coil magnetizes te string. Wen te string vibrates, it creates a time varying magnetic flux troug te coil and induces an emf in it. Te induced emf is ten amplified and fed to speakers.

6 L w w Ldr r I d. 0 A r I 0 Ldr da Lw A dr L da +w w IL ln 0 bt a I w L bt a t ln 0 w bl t d ln 0 E I ind A d.

7 As te wire moves, F qv Wic sets te carges in motion in te direction of F and leaves positive carges beind. As tey accumulate on te bottom, an electric field is set up inside. In equilibrium, F F qv e qe E v V El lv

8 A lx E d d lx l dx E lv I E R lv R If te bar is moved wit constant velocity, F app F Il P l v E F app v Ilv R R

9 F x ma dv m Il I lv R Te bar as a mass, m, and an initial velocity v i F Il dv m dv v l R l mr v v e i t v l mr 1

10 Te polarity of te induced emf is suc tat it tends to produce a current tat creates a magnetic flux to oppose te cange in magnetic flux troug te area enclosed by te current loop. As te bar is slid to te rigt, te flux troug te loop increases. Tis induces an emf tat will result in an opposing flux. Since te external field is into te screen, te induced field as to be out of te screen. Wic means a counterclockwise current

11 Suppose, instead of flowing counterclockwise, te induced current flows clockwise: Ten te force will be towards te rigt wic will accelerate te bar to te rigt wic will increase te magnetic flux wic will cause more induced current to flow wic will increase te force on te bar and so on All tis is inconsistent wit te conservation of energy

12 Rigt moving magnet increases flux troug te loop. It induces a current tat creates it own magnetic field to oppose te flux increase. Left moving magnet decreases flux troug te loop. It induces a current tat creates it own magnetic field to oppose te flux decrease.

13 Wen te switc is closed, te flux goes from zero to a finite value in te direction sown. To counteract tis flux, te induced current in te ring as to create a field in te opposite direction. After a few seconds, since tere is no cange in te flux, no current flows. Wen te switc is opened again, tis time flux decreases, so a current in te opposite direction will be induced to counter act tis decrease.

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15 Canging Magnetic Flux EMF Electric Field Inside a Conductor Tis induced electric field is non-conservative and time-varying E d W qe FE r qe E qe E r r d E r r d E 1 1 r d r E ds. d General Form of Faraday s Law

16 d E. ds d E. ds R R E r R E d r R ni sin t 0 max d E 0nImaxR r sin t r > R I( t) Imax ni 0 cos t ( t) 0nI max cos t E r d r r r ni sin t E 0 max 0nI max r sin t r < R

17 AC Generator DC Generator Acos Acos t d E N NA E NA max d cos t NA sin t A motor is a generator in reverse. A time-varying current is applied to te loop. Te resulting torque rotates te loop and te saft connected to it.

18 If a solid piece of conductor moves in and out of a magnetic field, circulating currents can be induced in te conductor. Tese currents rise from induction and obey Lenz s Law. Since tey result in undesirable energy transfer to internal energy, tey are generally minimized by layering or sectioning large metal components.

19 Reading Assignment Capter 3 Inductance WebAssign: Assignment 9