Faraday s law of induction

Transcription

1 Faraday s law of indction The emf e eqals the time rate of change of the magnetic flx e = - N DF B /Dt We saw one way of changing the magnetic flx this - sign is so important we re going to give it a name all to itself: Lenz s law here s another Fig. 20.4, p.623

2 Notice the direction of the crrent flow That s the - sign the direction of the indced emf is sch that it tries to prodce a crrent whose magnetic field opposes the change in flx thr the loop Lenz s law (the Idaho Repblican law ) s any change is resisted no matter what the direction

3 Notice the direction of the crrent flow I psh the magnet in; the coil is pshing back I pll the magnet ot; the coil is plling back

4 Lenz s law Sppose I have a condcting bar sliding on condcting rails, in a magnetic field pointing into the page If it slides to the right, what is the direction of the crrent what is the direction of the force? What is the magnitde of the emf indced? e = - DF B /Dt = - BDA/Dt = - BlDx/Dt = - Blv What is the magnitde of the crrent? I = e/r What is the magnitde of the force on the bar? F = IlB

5 Lenz s law What if the bar were sliding to the left? what is the direction of the indced crrent? what is the direction of the force on the bar? Lenz s law is jst a restatement of the law of conservation of energy notice how many things come back to conservation of energy

6 Motional emf Another way to think abot problem Let s jst concentrate on the condcting bar moving to the right There are condction electrons free to move and some of them will (which direction?) The movement of electrons creates an electric field in the condctor

7 Motional emf How large of an electric field? The forces balance evb = ee E = vb If the bar has a length l, what is the emf indced? e = El = Blv

8 Motional emf Now I allow the condcting bar to slide on some condcting rods. What happens? A crrent flow.

9 Faraday s law of indction The emf e eqals the time rate of change of the magnetic flx e = - N DF B /Dt F B = B A cosq F B can change by s B changing s A changing s q changing

10 A case where B and A stay the same bt q changes an electrical generator consists of a coil rotating inside of a constant magnetic field it prodces an emf that varies sinsoidally with time Fig , p.634

11 Electrical generator F B = B A cosq = B A cos wt e = - N DF B /Dt = - N B A w coswt Fig , p.635

12 emf from a generator e = - N DF B /Dt = - N B A w coswt e max = N B A w T = 2p/w

13 Generators and motors What s the difference between them? A generator trns mechanical work into electrical energy. A motor trns electrical energy into mechanical work. A motor is a generator rn in reverse.

14 Self-indctance Let s go back to the most basic of circits let s re-draw it Fig , p.637

15 What happens after I first close the switch? Before, we wold have said that the crrent instantly jmps to its final vale of e/r Bt now we know abot Faraday s law of indction (and Lenz s law) Think abot the circit as a loop with crrent flowing throgh it When I first close the switch, a crrent wants to flow in the direction indicated Bt that crrent creates a magnetic field in the loop Lenz s law says that change will be resisted (what is the change?) An emf will be created in the direction opposite the battery This is called self-indction. The emf prodced is called a self-indced emf.

16 Consider another example no indced emf indced emf indced emf Fig , p.638

17 Self-indctance Indced emf is given by e = -N DF B /Dt Flx F B is proportional to the magnetic field which is proportional to the crrent flowing So the emf mst be proportional to the rate of change of crrent e = -L DI/Dt note - sign still there L is the indctance of the circit

18 Units e = -L DI/Dt L = -e/(di/dt) [L] = [e]/([di]/[dt]) [L] = V. s/a 1 Henry = 1 V. s/a Joseph Henry ( ); American physicist who actally was the first to prodce an electric crrent with a changing magnetic flx bt a heavy teaching schedle prevented him from pblishing before Faraday

19 Indctance If I have a circit element with a large indctance, I indicate it by a symbol DV R = -IR Resistance is a measre of the opposition to the crrent e L = - LDI/Dt Indctance is a measre of the opposition to the change of crrent

20 Circit with an indctor Sppose I have the circit to the right What happens after I close the switch S? The crrent wants to start flowing, bt the indctance L resists this change e L = - LDI/Dt at moment switch is closed, all of battery emf is across indctor (and none across resistor) crrent gradally increases as e L decreases and more of battery voltage is across the resistor Kirchoff s loop rle e - IR - LDI/Dt = 0

21 RL circits At t=0, I=0 At t= a long time, I=e/R I=I o (1-e -t/t ) I o =e/r t=l/r (the time constant ) after one time constant, I = 63% of final vale

22 Eddy crrents Sppose I have a pendlm with a copper plate on the end that swings throgh a magnetic field Do I expect anything to happen? there s a change in magnetic flx throgh the copper as it swings into the magnetic field, so an emf will be indced and copper is a good condctor eddy crrents which direction?

23 Energy in magnetic fields We previosly saw that when we charged p a capacitor, there was an energy stored in the capacitor eqal to E = 1/2C(DV) 2 we can think of the energy as being stored in the electric field created inside the capacitor When we have a crrent flowing inside an indctor, there s an energy stored in the indctor E = 1/2LI 2 we can think of the energy as being stored in the magnetic field inside the indctor