Physics 212 Lecture 17

1. Physics 212 Lecture 17 Faraday’s Law

2. Music • Will I get points for this question? • Yes and no • Maybe • Who is “I”? You? You won’t get points. • I get The point • It’s a pointless question Physics 212 Lecture 23

3. Faraday’s Law: where and f is force / unit charge: A changing magnetic flux can drive current around a loop  electromagnetic battery! When B-dot-A changes, what “f” causes the EMF? • “A” or “dot” changes (moving or rotating loops) f = v x B = familiar magnetic force • B changes  f = E = induced electric field NEW TYPE OF ELECTRIC FIELD!Caused by dB/dt not charges; its field lines make loops!

4. A Flux Think ofFBas the number of field lines passing through the surface Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. B There are many ways to change this…

5. A Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. B Move loop to a place where the B field is different EMF caused by magnetic force: f = v x B

6. A Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. B EMF caused by magnetic force: f = v x B Rotate the loop

7. Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. B A EMF caused by magnetic force: f = v x B Rotate the loop

8. Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. B A EMF caused by magnetic force: f = v x B Rotate the loop

9. A Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. Nothing’s moving ...So no magnetic force … B Change the B field EMF caused by electric force: f = E dB/dt creates an electric field !often called an “induced E-field”

10. Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop.2) The emf will make a current flow if it can (like a battery). I

11. Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows generates a new magnetic field. I

12. Checkpoint 1 Suppose a current flows in a horizontal conducting loop in such a way that the magnetic fluxproduced by this current points upward. As viewed from above, in which direction is this current flowing?

13. dB/dt Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic field that created it  Lenz’s Law B

14. dB/dt Faraday’s Law: where In Practical Words: 1) When the fluxFBthrough a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic field that created it  Lenz’s Law B Demo

15. Checkpoint 2 A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conductingloop is entering the field as shown. At the instant shown, what is the direction of the additional flux produced by the current induced in the loop?

16. Checkpoint 3 A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conductingloop passes through the field from left to right as shown. The upward flux through the loop as a function of time is shown by the blue trace. Which of the red traces best represents the current induced in the loop as a function of time as it passes over the magnet? (Positive means counter-clockwise as viewed from above.)

17. Faraday’s Law: where Executive Summary: emf→current→field a) induced only when flux is changing b) opposes the change

18. Old Checkpoint 2 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet “Please do not display this in lecture but that picture on this checkpoint with the falling conducting loop looked a LOT McDonalds like french fries.” (copper is notferromagnetic) Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A. a > g B.a = g C. a < g

19. Old Checkpoint 2 F B O X B Like poles repel Ftotal < mg a < g A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet (copper is notferromagnetic) Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A. a > g B.a = g C. a < g This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced

20. Old Checkpoint 2 Looking down B B I I IL X B points UP Ftotal < mg a < g A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet HOW IT WORKS (copper is notferromagnetic) Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A. a > g B.a = g C. a < g This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Demo ! dropping magnets e-m cannon Main Field produces horizontal forces “Fringe” Field produces vertical force

21. Calculation y A rectangular loop (height = a,length = b,resistance = R,mass = m) coasts with a constant velocity v0in + x direction as shown. At t =0, the loop enters a region of constantmagnetic field Bdirected in the –z direction. What is the direction and the magnitude of the force on the loop when half of it is in the field? B x x x x x x x x x x x x x x x x x x x x x x x x x x x x b a v0 x • Conceptual Analysis • Once loop enters B field region, flux will be changing in time • Faraday’s Law then says emf will be induced • Strategic Analysis • Find the emf • Find the current in the loop • Find the force on the current

22. y y B B x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x b b a a v0 v0 x x Change in Flux = dFB = BdA = Bav0dt Calculation A rectangular loop (height = a,length = b,resistance = R,mass = m) coasts with a constant velocity v0in + x direction as shown. At t =0, the loop enters a region of constantmagnetic field Bdirected in the –z direction. What is the magnitude of the emf induced in the loop just after it enters the field? (A) e = Babv02(B) e = ½ Bav0(C) e = ½ Bbv0(D) e = Bav0(E) e = Bbv0 a The area in field changes by dA =v0dt a In a time dtit moves by v0dt

23. Calculation y B x x x x x x x x x x x x x x x x x x x x x x x x x x x x b a v0 x What is the direction of the current induced in the loop just after it enters the field? (A) clockwise(B) counterclockwise(C) no current is induced Induced emf produces flux out of screen y A rectangular loop (height = a,length = b,resistance = R,mass = m) coasts with a constant velocity v0in + x direction as shown. At t =0, the loop enters a region of constantmagnetic field Bdirected in the –z direction. B x x x x x x x x x x x x x x x x x x x x x x x x x x x x b a v0 x emf is induced in direction to oppose the change in flux that produced it Flux is increasing into the screen

24. Calculation Force on a current in a magnetic field: y B x x x x x x x x x x x x x x b v0 • Force on top and bottom segments cancel (red arrows) a • Force on right segment is directed in –x direction. I x y A rectangular loop (height = a,length = b,resistance = R,mass = m) coasts with a constant velocity v0in + x direction as shown. At t =0, the loop enters a region of constantmagnetic field Bdirected in the –z direction. B x xxxxxx x xxxxxx x xxxxxx x xxxxxx b a v0 x What is the direction of the net force on the loop just after it enters the field? (A) +y(B) -y(C) +x (D) -x

25. Calculation since y B x x x x x x x x x x x x x x b v0 a F I ILB x y A rectangular loop (height = a,length = b,resistance = R,mass = m) coasts with a constant velocity v0in + x direction as shown. At t =0, the loop enters a region of constantmagnetic field Bdirected in the –z direction. B x x x x x x x x x x x x x x x x x x x x x x x x x x x x b a v0 x What is the magnitude of the net force on the loop just after it enters the field? e = Bav0 (A) (B) (C) (D)

26. Follow-Up Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ? (A) (B) (C) D) (E) X X X B x x x x x x x x x x x x x x b v0 a Fright I t = dt: e = Bav0 y A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. What is the velocity of the loop when half of it is in the field? B x x x x x x x x x x x x x x x x x x x x x x x x x x x x b v0 a x This is not obvious, but we know v must decrease Why? Fright points to left Acceleration negative Speed must decrease

27. Follow-Up where Claim: The decrease in kinetic energy of loop is equal to the energy dissipated as heat in the resistor. Can you verify?? y A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. What is the velocity of the loop when half of it is in the field? B x x x x x x x x x x x x x x x x x x x x x x x x x x x x b v0 a x e = Bav0 Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ? (A) (D) • Why (D), not (A)? • F is not constant, depends on v Challenge: Look at energy