Physics 227: Exam 2 Information

Transcription

1 Physics 227: Exam 2 Information Note: exam 2: 16 questions covering chapters Thursday, Nov 17, 2011, 9:40 PM - 11:00 PM Room assignments: A-I Arc 103 J-M SEC probably starts 9:50 or 10:00. N-R PLH S-Z Beck Auditorium, Livingston Campus!!! (NOT Hill 114) Anyone with a conflict should contact Prof. Cizewski ASAP Bring pencils, 1 formula sheet w/ anything you want, NO calculators or other electronics needed or allowed!

2 Physics 227: Lecture 18 Induction, Faraday s Law, Lenz s Law, Motional EMF Lecture 17 review: Magnetization: B = B 0 + μ 0 M = (1+χ) B 0 = KB 0. Ferromagnets: χ Paramagnets: χ Diamagnets: χ Domains grow with applied B field. Hysteresis. Curie s Law and Curie temperature. Magnetostriction. Displacement current in capacitor: I D = I.

3 Maxwell s Equations In the late 1800s the knowledge of electric and magnetic fields was summarized with Maxwell s Equations: E = ρ 0 B =0 B = µ 0 0 E E = B t t + µ 0 J Gauss s Law: electric fields start/stop on charges. There are no magnetic charges. Changing magnetic fields generate electric fields. Today+Thursday! Magnetic fields result from currents and changing electric fields. E d A = q enclosed B ds = 1 c 2 dφ E 0 B d A =0 E ds = dφ B dt dt + µ 0 i enc

4 Demos Changing magnetic flux leads to emf leads to currents. Phets, demos...

5 An EMF Demo These demos done last Monday!

6 Faraday s Law Changing the magnetic field changes the flux, leading to an emf that causes a current in the loop. Quantitatively, we use Faraday s Law: ε = ε = dφ B dt E d l = dφ B dt = d B d A dt Lenz s Law: Induced E field causes a current that opposes the change.

7 Faraday s Law iclicker Consider a single closed loop in the magnetic field. The B-field is ramped up at the rate of 0.01 T/s. The area of the loop is 0.1 m 2. What is the magnitude of the emf around the loop? emf = dφ/dt = d(ab)/dt = A db/dt = 0.1 m 2 x 0.01 T/s = V A. 0 V - no voltage around a loop. B V. C V. D. 0.1 V. E. 10 V.

8 Lenz s LAw The resulting emf causes a current in the loop that generates a B field that opposes the change. N connected loops increases the flux and emf by a factor of N.

9 Rotating Coil Consider a loop of area A in a constant B field. The loop rotates at a frequency ω about the axis shown. What is the emf around the loop? φ B = B d A = BAcos(ωt) ε = dφ B dt = ωba sin(ωt)

10 Alternator An alternator can be a loop rotating in a constant B field region, producing a sinusoidal emf (ε = ωba sin(ωt)) and a sinusoidal current. Could we keep the loop fixed and rotate a magnet instead? Why would this be better or worse?

11 Commercial Alternator An electromagnet on a shaft goes into the center of the armature shown. Use coils with many loops to increase the emf, or the B field generated.

12 DC Generator A few classes ago, we sent a current through the loop to the left, and put it in a magnetic field, to obtain a DC motor. Now we rotate it, in a constant B field, and we have a DC generator. The emf generated is ε = ωba sin(ωt), which averages to 2ωBA/π. Use of multiple coils and commutators makes the emf more nearly constant. Alternators generate AC, generators generate DC!

13 Linear Generator Earlier we saw that a current through a ``sliding bar in a region of magnetic field causes the bar to move. Now we have a loop with a movable side in a field, and we move the side at constant velocity. ε = dφ B dt = B da dt = BLv

14 Power in the Generator From the emf, what is the power needed? P = ε 2 /R = B 2 L 2 v 2 /R We can also calculate this from the force applied, and P = Fv. P = Fv = ILBv = BLv R LBv = B2 L 2 v 2 /R

15 Power Motors, generators, and alternators convert between electrical energy and mechanical energy. The energy is not free, and the processes are less than 100% efficient, due to mechanical friction of moving parts, resistance of wires,...

16 Lenz s Law iclicker The coil is squeezed. What is the direction of the emf around the loop? A. 0 V - no emf around a loop. B. CW. C. CCW. Squeezed coil has less area. Flux into page reduced. EMF will generate a CW current to oppose reduction in flux. D. Huh? This question is unfair! It requires the RH rule! :(

17 Motional EMF F M = qvb. F E = qe = qε/l. F M = F E qvb = qε/l ε = vbl is the motional emf. Generalizing... dε = v B d l Around a closed loop... ε = v B d l

18 Faraday Disk Dynamo = DC Homopolar Generator dε = v B d l ε = ωrbdr = ωbr 2 /2

19 Motional EMF I would accept either C or D. E might be true, but it is not the physics answer. The motional emf for the rod is vbl. The Faraday s Law emf for the loop is also vbl. Which of the following is true? A. The total emf in the loop in 2vBL. B. The total emf in the loop is 0 - the emfs are opposed. C. These are two different ways of getting to the same physics. D. You get one emf or the other, not both - they are different and don t both apply at the same time. E. This whole thing confuses me.

20 Thank you. See you Thursday.