Ch 34: Faraday’s Experiment

1. Ch 34: Faraday’s Experiment • Trying to induce a current using magnetic fields • No induced current in “Y” loop with a DC circuit • Saw a current when opening and closing the switch (changing the magnetic field)

2. Electromagnetic Induction Faraday’s Law - An induced emf is produced by a changing magnetic field • Can move magnet or loop • Direction of motion controls direction of current • No movement, no current

4. Predict the direction of the induced current

5. Motional EMF • A current is caused by an electric field • Current continues until FB = FE FE = qE FB = qvB qE = qvB E = vB

7. Which is the correct picture?

8. E = Blv (assumes B ┴ to v)

9. An airplane travels at 1000 km/hr in a region where the earth’s magnetic field is 5 X 10-5T (vertical). Calculate the potential difference between the wing tips if they are 70 m apart. 1000 km/hr = 280 m/s E = Blv E = (5 X 10-5T )(70 m)(280 m/s) = 1.0 V

10. A metal bar of length l rotates in a magnetic field B that is perpendicular to the plane of rotation. It rotates at an angular speed of w. a. Determine the potential difference between the two ends of the bar (HINT: substitute for w, and then integrate from 0 to l, the pivot to the end)

11. Motional EMF • Moving a bar or wire produces charge separation • If looped, produces a current • Bar doesn’t want to move (Lenz’s law), must exert a force • Remember Fmag = IlB Fpull = vl2B2 l = length R R = resistance

12. Example Consider the following set-up. The bar is 10.0 cm long. • Calculate the current needed for the bulb (P = IV) • Calculate the resistance of the bulb • Calculate the speed needed to achieve this current. (E = Blv) • Calculate the force required for the pull

14. EMF in a Moving Conductor • Slide a conducting bar on the wire loop • Increasing area • What direction is the induced current? (right hand rule)

16. Moving Conductor: Ex 2 Blood contains charged ions. A blood vessel is 2.0 mm in diameter, the magnetic field is 0.080 T, and the blood meter registers a voltage of 0.10 mV. What is the flow velocity of the blood?

17. E = Blv v = E /Bl v = (1.0 X 10-4 V) (0.080 T)(0.0020m) v = 0.63 m/s

18. Magnetic Flux (flow) FB = Magnetic Flux FB = BAcosq B = Magnetic Field (T) A = area passes through (m2) q = Angle ┴ to surface

19. If B ┴ to surface • Cos 0o = 1 • Maximum flux If B || to surface • Cos 90o = 0 • No flux

20. Faraday’s Law of Induction E = -NDFB Dt N = number of loops in a wire DFB/Dt= change in magnetic flux over time So why is it negative?

21. Lenz’s Law An induced current’s magnetic field opposes the original change in flux • Always tries to keep magnetic field inside loop constant. • Use right-hand rule to predict direction of current. • Curve your fingers around the loop • v is direction of the induced current

22. Lenz’s Law: Ex 1 Why is the direction of the current as indicated? • Area is decreasing • Flux is decreasing • Induced current points into paper through ring

23. Lenz’s Law: Ex 2 What will happen to the current if you allow the ring to relax to its original shape? • Larger area • Induced I will reverse direction

24. 3 Ways to cause an emf • Change the magnetic field • Change area of loop • Rotate the loop (or magnet) No flux Maximum flux

26. Lenz’s Law: Ex 3a Predict the direction of the induced current in the following situations

27. Counterclockwise current • Magnet is going in (north in), need a current pointing north out through the loop

29. No current • Magnetic flux is || to the loop

31. Magnetic field decreasing • Counterclockwise current to increase it

33. Decreasing flux • Clockwise current induced

34. B

35. Initially no flux • Flux increases to left • Counterclockwise current

36. A long straight wire carries a current I as shown. • Predict the direction of the magnetic field inside the adjacent loop. • As the wire is pulled away from the loop, predict the direction of the induced current.

37. Motional EMF E = DFB Dt E = BDA Dt E = BlvDt Dt E = Blv (assumes B ┴ to v)

38. Lenz’s Law: Ex 4 A square coil of 100 loops is quickly pulled from the magnetic field as shown in 0.10 s. Calculate the change in flux.

39. FBfinal =0 FBinitial = BAcos0 FBinitial = (0.60 T)(0.050m)2(1) FBinitial = 0.0015 Wb DF = FBfinal – Fbinitial DF = 0 – 0.0015 Wb = -0.0015 Wb

40. What Voltage and current are produced in the loop (assume resistance = 100 W) E = -NDFB Dt E = -(100)(-0.0015 Wb) = 1.5 V 0.10 s V = IR I = V/R = 1.5 V/100 W= 0.015 A (15 mA)

41. Faraday’s Law of Induction E = -NDFB Dt E = NvlB (V = IR) IR = NvlB I = NvlB R

42. Faraday’s Law: Ex 1 A patient neglects to remove a 6.0 cm copper bracelet (R = 0.010 W) before getting an MRI. The magnetic field changes from 1.00 T to 0.40 T in 1.2 s. Assume the field passes perpendicular to the bracelet. • Calculate the magnetic flux for both T’s (FB = Bacosq) • Calculate the voltage through the bracelet based on the change in flux. • Calculate the current through the bracelet

43. Induced Electric Fields Coulomb vs. non-Coulomb • Coulomb Electric field – created by positive and negative charges • Non-Coulomb – created by a changing magnetic field Both exert forces on charges (F = qE)

44. Another version of Faraday’s Law

45. Electric Field outside a solenoid

46. A 4.0 cm diameter solenoid is wound with 2000 turns/meter. The current oscillates at 60 Hz and has an amplitude (maximum) of 2.0 A. Here are some equations to help you: B = m0nI I = I0sinwt • Determine the electric field inside the solenoid. • Determine the maximum electric field inside the solenoid.

47. Electric Generators (Dynamo) • Generator is the inverse of a motor • AC Generator shown • Rotation through magnetic field induces I • Current flows first one way, then the other

48. Segments ab and cd are moving conductor • (Side segments have force in wrong direction) E = Blv┴ v┴ = vsinq E = 2NBlvsinq

49. Can consider angular rotation q = wt v = wr = w(h/2) h = length of ad or bc E = 2NBlvsinq E = 2NBlw(h/2) sin wt lh = Area E = wNBAsin wt

50. Remember w = 2pf f = frequency (Hertz) w (radians/s)