1. Physics 212 Lecture 17, Slide 1 Physics 212 Lecture 17 Faraday’s Law

2. Physics 212 Lecture 17, Slide 2 Motional EMF Change Area of loop Change magnetic field through loop Change orientation of loop relative to B In each case the flux of the magnetic field through the circuit changes with time and an EMF is produced. EMF

3. Physics 212 Lecture 17, Slide 3 B Rotate the loop,change flux, generate emf.

4. Physics 212 Lecture 17, Slide 4 Move loop to a place wherethe B field is different, change flux, generate emf. B2B2B2B2 v B1B1B1B1

5. Checkpoint 1a Physics 212 Lecture 17, Slide 5 The flux is NOT changing The flux is NOT changing B does not change B does not change the area does not change the area does not change the orientation of B and A does not change the orientation of B and A does not change Motional emf is ZERO Motional emf is ZERO v X B = 0 v X B = 0 no charge separation no charge separation no E field no E field no emf no emf A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Suppose the loop is moving to the right. The current induced in the loop is: A. zeroB. clockwiseC. counterclockwise

6. Physics 212 Lecture 17, Slide 6 Current changes direction every time the loop becomes perpendicular with the B field emf ~ d  /dt (B  dA = max)  d/dt (B  dA ) = 0 (B  dA = max)  d/dt (B  dA ) = 0 X O B dA X OB dA Checkpoint 1c Now suppose that the loop is spun around a vertical axis as shown, and that it makes one complete revolution every second. The current induced in the loop: A. Is zero B. Changes direction once per second C. Changes direction twice per second

7. Faraday’s Discovery True no matter how we change the flux. In fact, the circuit may be stationary (no motional EMF) and only the B-field changes with time. An EMF is still produced. This implies that: Faraday’s Law

8. Physics 212 Lecture 17, Slide 8 B(t) decreasing Change the B field in time so flux changes. Induce an emf nnd therefore an Electric field. This emf tries to oppose the change in flux. (Lenz’s Law) Induces an E field even if there is no circuit there! there is no circuit there!

9. Physics 212 Lecture 17, Slide 9 Checkpoint 1b Motional emf is ZERO Motional emf is ZERO Circuit is stationary ! Circuit is stationary ! HOWEVER: The flux is changing HOWEVER: The flux is changing B decreases in time B decreases in time current induced to oppose the flux change current induced to oppose the flux change clockwise current tries to restore B that was removed clockwise current tries to restore B that was removed X X X X X X X X Looking from right Clockwise current tries to restore B Checkpoint 1b A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Now suppose the that loop is stationary and that the magnetic field is decreasing in time. The current induced in the loop is: A. zero B. clockwiseC. counterclockwise

10. Physics 212 Lecture 17, Slide 10 (copper is not ferromagnetic) This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced F total < mg a < g X O B B Like poles repel F Checkpoint 2 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet 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 > gB. a = gC. a < g

11. Physics 212 Lecture 17, Slide 11 Main Field produces horizontal forces “Fringe” Field produces vertical force I Looking down I BB IL X B points UP F total < mg a < g HOWITWORKS (copper is not ferromagnetic) This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Checkpoint 2 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet 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 > gB. a = gC. a < g

12. Physics 212 Lecture 17, Slide 12Calculation 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 y x v0v0 a 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 B A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v 0 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 direction and the magnitude of the force on the loop when half of it is in the field?

13. Physics 212 Lecture 17, Slide 13 What is the magnitude of the emf induced in the loop just after it enters the field? (A) (B) (C) (D) (E) (A)  = Babv 0 2 (B)  = ½ Bav 0 (C)  = ½ Bbv 0 (D)  = Bav 0 (E)  = Bbv 0 In a time dt it moves by v 0 dt Change in Flux = d  B = BdA = Bav 0 dt Calculation A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v 0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y x v0v0 a 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 B y x v0v0 a 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 B The area in field changes by dA = v 0 dt a a

14. Physics 212 Lecture 17, Slide 14 What is the direction of the current induced in the loop just after it enters the field? (A) (B) (C) (A) clockwise (B) counterclockwise (C) no current is induced Flux is increasing into the screen emf is induced in direction to oppose the change in flux that produced it Induced emf produces flux out of screen Calculation y x v0v0 a 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 B A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v 0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y x v0v0 a 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 B

15. Physics 212 Lecture 17, Slide 15 What is the direction of the net force on the loop just after it enters the field? (A) (B) (C) (A) +y (B) -y (C) +x (D) -x x y v0v0 a b x x x x x x x x x x x x x x x x x x x x x B I Force on top and bottom segments cancel (red arrows) Force on top and bottom segments cancel (red arrows)Calculation y x v0v0 a 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 B A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v 0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. Force on right segment is directed in –x direction. Force on right segment is directed in –x direction. Force on a current in a magnetic field:

16. Physics 212 Lecture 17, Slide 16 x y v0v0 a b x x x x x x x x x x x x x x x x x x x x x B I F What is the magnitude of the net force on the loop just after it enters the field? (A) (B) (C) (A) (B) (C) (D)  = Bav 0Calculation y x v0v0 a 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 B A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v 0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. ILB since

17. Physics 212 Lecture 17, Slide 17Follow-Up A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v 0 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? y x v0v0 a 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 B t = dt  = Bav 0 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) (A) (B) (C) D) (E) This is not obvious, but we know v must decrease Why? v0v0 a b x x x x x x x x x x x x x x x x x x x x x B I F right F right points to left Acceleration negative Speed must decrease X XX

18. Physics 212 Lecture 17, Slide 18Follow-Up A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v 0 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? Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ? y x v0v0 a 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 B  = Bav 0 (A) (D) (A) (D) Why (D), not (A)? – –F is not constant, depends on v Challenge: Look at energy Claim: The decrease in kinetic energy of loop is equal to the energy dissipated as heat in the resistor. Can you verify?? where