1. Induction II

3. Law of Induction The magnitude of the induced emf in a circuit is equal to the rate at which the magnetic flux through the circuit is changing with time. If coil has N turns

4. Change in flux may be due to Change in magnetic field Change in the area Both.

5. Lenz’s law The flux of the magnetic field due to the induced current opposes the change in the flux that causes the induced current.

6. Motional EMF

7. Induced current flows in the loop External agent pulls the loop with constant speed

9. F 1 is the net magnetic force If external agent pulls with constant speed F ext = F 1 = I ind DB Mechanical power P = F 1 v

10. The power expended by the external agent

11. A conducting rod of length L is being pulled along horizontal, frictionless and conducting rails. A uniform magnetic field fills the region in which the rod moves. Assume B = 1.18 T, L = 10.8 cm, v = 4.86 m/s, resistance of rod as 415 m .

12. Find Induced emf  = BLv = 0.619 V Current in the conducting loop. I =  /R = 1.49 A Assume B = 1.18 T, L = 10.8 cm, v = 4.86 m/s resistance of rod as 415 m 

13. At what rate does the internal energy of rod increase? P =  I ind = 0.922 W Force that must be applied by external agent to maintain its motion F = ILB = 0.190 N At what rate does this force do work on rod? P = F v = 0.922 W

14. Eddy Currents  An emf and a current are induced in a circuit by a changing magnetic flux.  When the magnetic flux through a large piece of conductor changes, induced current appear in the material in small loops.  These are called eddy currents as they induce in little swirls/eddies.

16. http://www.ndt- ed.org/EducationResources/HighSchool/Ele ctricity/eddycurrents.htm http://www.ndt- ed.org/EducationResources/HighSchool/Ele ctricity/eddycurrents.htm http://www.ndt- ed.org/TeachingResources/NDT_Tips/Lenz Law.htm http://www.ndt- ed.org/TeachingResources/NDT_Tips/Lenz Law.htm

17. Eddy currents and energy loss They can increase internal energy and thus temperature of the material Big eddy currents larger energy loss Materials which are subjected to magnetic fields are often constructed in many small layers.

19. Eddy currents slow down the motion of the conductor

20. A cylindrical bar magnet is dropped down a vertical aluminum pipe of slightly large diameter. It takes several seconds to emerge at the bottom, whereas, identical piece of unmagnetized iron makes the trip in a fraction of a second. Explain why magnet falls more slowly?? Ans: delay is due to forces exerted on the magnet by induced eddy currents in the pipe.

21. Advantage Heating effect can be used in induction furnace.

22. Magnetic field cannot force a stationary charge to move. Then why the charges move? Why there is an induced current?

23. Induced electric fields A changing magnetic field induces an electric field.

24. Induced electric field exists, even when ring is removed. It is always tangential.

25. Some facts The driving force for induced currents is induced E-field It exists, even when ring is removed. It has no radial component. As real as that might be setup by a real stationary charge.

27. In the static case, Faraday’s law reduces to

28. You can not define a potential for an induced electric field.

29. A uniform magnetic field B(t) pointing straight up fills the shaded circular region. If B is changing with time what is the induced electric field ? B(t)

30. r If B is increasing with time, induced current will run clockwise as look from above.

31. A line charge is glued onto the rim of a wheel of radius R, which is then suspended horizontally. It is free to rotate. The spokes are made of wood. In the central region out to radius a there is a uniform magnetic field pointing up. Now someone turns the field off. What happens? ds B

32. Torque on the segment ds

33. Two parallel loops of wire are shown with common axis. Smaller loop is above the larger loop by a distance x>>R. Magnetic field due to current i in the larger loop is constant through the smaller loop and equal to the value on the axis. Suppose x is increasing with constant rate.

34. (a) Determine the flux across the area bounded by smaller loop as a function of x.

35. Compute the emf generated in the smaller loop Direction of current is anticlockwise as seen from above.

36. Two straight conducting rails form an angle  where their ends are joined. A conducting bar in contact with the rails and forming an isoscale triangle with them, starts at the vertex at time t = 0 and moves with constant velocity v to the right. A magnetic field points out of the page.

37. Find emf induced as a function of time.

38. A square loop of wire lies on a table, a distance s from a very long straight wire, which carries a current I. If someone pulls the loop away from the wire at speed v, what emf is generated? s a a a

39. Flux through the loop s a a a

40. Direction of induced current is anticlockwise.