Electromagnetic Induction

1. Electromagnetic Induction

2. 21.7 Magnetic Fields Produced by Currents • In 1820, H.C. Oersted discovered that a current in a wire caused a deflection in a magnet. • This led to the conclusion that moving charges were magnets, producing their own magnetic field and exerting forces on other magnets. • It seemed natural for scientists to investigate the opposite: Can a magnet generate a potential difference and thus cause current flow, in much the same way as a battery?

3. “Induced” Current • A current creates a magnetic field. • Is the opposite true? • Can a magnetic field create, or induce a current? • In 1831, Michael Faraday made an exciting discovery

4. Faraday’s Discovery • To test this hypothesis, Faraday used 2 separate circuits that were not connected and wrapped each around an iron ring that did not conduct electricity. • He thought by closing the switch on the left, the magnetic field of the left wire would magnetize the iron ring, which in turn might induce a current in the wire on the right. • But no luck, as the meter shows.

5. Faraday’s Discovery • Disappointed, he shut down for lunch. • But when he opened the switch to cut off the current in the left circuit, the meter suddenly moved, showing a momentary current in the wire on the right. • It quickly went back to zero.

6. Faraday’s Discovery • Baffled, he closed the switch again. • And noticed that the meter jumped again momentarily, and this time the meter needle went the other way. • I bet he actually did it a bunch of times before he noticed that it went the other way..

7. Faraday’s Law • Faraday found that he could induce a current in a closed coil of wire with an external magnetic field, but only if the magnetic field through the coil is changing. • This is an informal statement of Faraday’s Law. • A moving magnetic field causes charge to flow, just as moving charge causes a magnet to deflect.

8. 22.1 Induced Emf and Induced Current There are a number of ways a magnetic field can be used to generate an electric current. It is the changing magnetic field that produces the current.

9. A square loop of copper wire is pulled through a region of constant magnetic field. In which case, if any, does current flow? A. 2,3,4 B. None C. 2,4 D. All 1 2 3 4

10. 22.1 Induced Emf and Induced Current We know that a current is induced in the presence of a changing magnetic field. How do we calculate the magnitude and direction of the current? To do so, we must discuss a quantity called the magnetic flux, Φ.

11. 22.3 Magnetic Flux GRAPHICAL INTERPRETATION OF MAGNETIC FLUX • We can think as the magnetic flux as proportional to the number of magnetic field lines that pass through a surface. We can change the magnetic flux by: • changing the magnetic field strength(B) as shown • changing the size of the loop • changing the angle between the normal to the loop and the direction of B

12. Magnetic Flux due to an external magnetic field Φm = AB cos θ A = cross-sectional area of the loop (m2 ) B = strength of magnetic field (Tesla) θ = angle between B, and normal to A Units: 1 weber = 1Wb = 1Tm2

13. Rank the magnitude of magnetic flux that passes through the coil, shown below (edge view) in three different orientations relative to an external magnetic field. Rank from greatest flux to least. • 1,2,3 b. 3,2,1 c. (1,3), 2 d.(3,1), 2

14. Magnetic Flux A uniform magnetic field has a magnitude of 0.078 T and is uniform over a circular surface of radius 0.10 m. The field is oriented at an angle of 25˚ with respect to the normal of the surface. What is the magnetic flux through the surface?

15. Magnetic Flux A uniform magnetic field has a magnitude of 0.078 T and is uniform over a circular surface of radius 0.10 m. The field is oriented at an angle of 25˚ with respect to the normal of the surface. What is the magnetic flux through the surface? Answer: 2.2 x 10-3 Wb

16. Change in Magnetic flux A long, narrow rectangular loop of wire is moving toward the bottom of the page with a speed of 0.019 m/s (see the drawing). The loop is leaving a region in which a 2.1 T magnetic field exists; the magnetic field outside this region is zero. During a time of 1.0 s, what is the magnitude of the change in the magnetic flux?

17. Change in Magnetic flux A long, narrow rectangular loop of wire is moving toward the bottom of the page with a speed of 0.019 m/s (see the drawing). The loop is leaving a region in which a 2.1 T magnetic field exists; the magnetic field outside this region is zero. During a time of 1.0 s, what is the magnitude of the change in the magnetic flux? Ans: .00319 Tm2 or Wb

18. 22.4 Faraday’s Law of Electromagnetic Induction • Faraday found that he could induce a current in a closed coil of wire with an external magnetic field, but only if the magnetic field through the coil is changing. This is an informal statement of Faraday’s Law. • The formal statement relates the changing magnetic flux to an induced emf (ε), which is the potential difference that causes a current to flow in a closed conductor. The magnitude of ε, the emf, induced in a coil of N loops is: SI Unit of Induced Emf: volt (V)

19. 22.4 Faraday’s Law of Electromagnetic Induction Example 5 The Emf Induced by a Changing Magnetic Field A coil of wire consists of 20 turns each of which has an area of 0.0015 m2. A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is 0.050 T and 0.10s later, it has increased to 0.060 T. Find the average emf induced in the coil during this time.

20. (Worksheet) Flux Ranking Task

21. (Worksheet)Changing Flux

22. An MRI Magnetic resonance imaging (MRI) is a medical technique for producing pictures of the interior of the body. The patient is placed within a strong magnetic field. One safety concern is what would happen to the positively and negatively charged particles in the body fluids if an equipment failure caused the magnetic field to be shut off suddenly. An induced emf could cause these particles to flow, producing an electric current within the body. Suppose the largest surface of the body through which flux passes has an area of 0.026 m2 and a normal that is parallel to a magnetic field of 3.5 T. Determine the smallest time period during which the field can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V.

23. An MRI Magnetic resonance imaging (MRI) is a medical technique for producing pictures of the interior of the body. The patient is placed within a strong magnetic field. One safety concern is what would happen to the positively and negatively charged particles in the body fluids if an equipment failure caused the magnetic field to be shut off suddenly. An induced emf could cause these particles to flow, producing an electric current within the body. Suppose the largest surface of the body through which flux passes has an area of 0.026 m2 and a normal that is parallel to a magnetic field of 3.5 T. Determine the smallest time period during which the field can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V. Ans: 9.1 s

24. A current-carrying wire is pulled away from a copper wire loop as shown. As a result, an emf (and therefore a current) is induced in the loop. To maximize the emf, we should: • pull the wire away from the loop more slowly • pull the wire away from the loop more quickly • push the wire towards the loop at the same speed.

25. Lenz’s Law • There is an induced current in a closed conducting loop only if the magnetic flux is changing (either B, A or θ). The direction of the induced current is such that the induced magnetic field opposes the change in flux.

26. Using Lenz Law • Determine the direction of the external magnetic field. • Determine how the flux is changing. Is it increasing, decreasing, or staying the same? • Determine the direction of an induced magnetic field that will oppose the change in the flux. • Increasing: induced magnetic field points opposite the external magnetic field. • Decreasing: induced magnetic field points in the same direction as the external magnetic field. • Constant: no induced magnetic field. 4. Determine the direction of the induced current. Use the right-hand rule.

27. Lenz’s Law An induced current in a coil or loop can be created 2 ways: • Change the size or orientation of the coil in a stationary magnetic field. • Change the strength of the magnetic field through a stationary circuit. Both of these create a changing magnetic flux.

28. The current exists because the changing magnetic flux has induced an emf. In a closed circuit with a resistance, R: I = ε/R The current is a consequence of the induced emf. The emf is a consequence of changing flux (Φm )

29. http://phet.colorado.edu/en/simulation/faraday

30. Lenz’s Law An external magnetic field, B is directed into the page. A sliding rail completes the circuit. The rail is pushed to the right, increasing the area of the circuit.

31. Lenz’s Law In which direction is the induced magnetic field? • into the page • out of the page • zero, since field is stationary • in the direction of the moving rail

32. Lenz’s Law

33. A current-carrying wire is pulled away from a copper wire loop as shown. As a result, an emf (and therefore a current) is induced in the loop. in what direction is the current? • clockwise • counterclockwise • No current

34. Is the induced current cw, ccw or zero? • The external magnetic field is increasing • The external magnetic field is decreasing • The right side of the loop turns into the page • The left side of the loop turns into the page

35. Positive (+) current comes out the top of the loop and enters the bottom. Negative (-) current comes out the bottom of the loop and enters the top. For A and B, and C is the current +, -, or zero? • A. The magnet is pushed into the loop. • The magnet is pulled back to the left. • The loop turns so the normal is in the plane of the page. • If the magnet is pulled out more loop more rapidly than in A, does the current increase, decrease or stay the same?