# LECTURE 23 INDUCED EMF. Instructor: Kazumi Tolich

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1 LECTURE 23 INDUCED EMF Instructor: Kazumi Tolich

2 Lecture 23 2 Reading chapter 23.1 to Induced emf Magnetic flux Faraday s law Lenz s law

3 Quiz: 1 3 Consider the circuits shown. Which of the following statements is/are correct? Choose all that apply. A. The current induced in the secondary circuit flows in the same direction when the switch is closed and opened. B. The current induced in the secondary circuit flows in the opposite direction when the switch is closed and opened. C. There is no current in the secondary circuit no matter what is happening with the primary circuit. D. There is no current in the secondary circuit a long time after the switch is closed.

4 Quiz: 23-1 answer/demo: 1 4 The current induced in the secondary circuit flows in the opposite direction when the switch is closed and opened. There is no current in the secondary circuit a long time after the switch is closed. Current is induced in the secondary circuit while the current in the primary circuit is changing. The induced current flows in opposite directions depending on whether the magnetic field is increasing or decreasing. Changing magnetic field creates induced emf.

5 Induced current by a moving magnet/demo: 2 5 A coil experiences an induced current when the magnetic field passing through it varies. The direction of the induced current depends on the velocity direction of the magnet.

6 Quiz: 2 6 Each figure shows an edge view of a circular loop placed in a uniform magnetic field. The dashed line shows the direction normal to the loop area. Rank the cases according to the amount of the magnetic field penetrating the area of the loop assuming they are identical loops, smallest first. Case A Case B Case C Case D

7 Quiz: 23-2 answer 7 D < C < B < A The numbers of field lines enclosed by the loop is different depending on the orientation of the loop relative to the magnetic field. Case A Case B Case C Case D

8 Magnetic flux 8 Magnetic flux is used in the calculation of the induced emf. Magnetic flux is the measure of the amount of magnetic field penetrating a given area. Magnetic flux is defined by Φ = BA cos θ B is the magnetic field that go through the surface A.

9 Faraday s law & Lenz s law/demo: 3 9 Faraday s law states: an emf, E, is induced in a conducting coil with N loops if the magnetic flux Φ through the coil changes with time. E = N Φ t Demo: wire and magnet Lenz s law tells the positive direction of the induced emf, represented by the minus sign in Faraday s law. The direction of the induced current is such that the induced magnetic field opposes the change in the flux.

10 Quiz: 3 10 Each figure shows an edge view of a circular conductive loop placed stationary in a uniform magnetic field. The dashed line shows the direction normal to the loop area. Rank the cases according to the amount of the current flowing in the loop assuming they are identical loops, smallest first. Case A Case B Case C Case D

11 Quiz: 23-3 answer 11 A = B = C = D Since the loops are stationary in the applied magnetic field, the magnetic flux is not changing. So, in all cases, the induced emf is zero. And no current flows in the loop.

12 Quiz: 4 12 A wire loop is placed in a magnetic field that is perpendicular to its plane. The field varies with time as shown. Rank the six regions of time in order of increasing magnitude of the induced emf.

13 Quiz: 23-4 answer 13 D = F < A < B < C < E E = N 5 6 = N 78 9:; < 6 = A 7 6 The magnitude of the induced emf is proportional to the steepness of the graph.

14 Quiz: 5 14 A gold ring is dropped and allowed to fall between the poles of a horseshoe magnet. Which of the following statements is correct? A. There is no current in the ring during the entire fall of the ring. B. The direction of the current in the ring is always clockwise throughout the fall. C. The direction of the current in the ring is always counterclockwise throughout the fall. D. The direction of the current in the ring is initially clockwise, and flips to counterclockwise as it passes the magnet. E. The direction of the current in the ring is initially counterclockwise, and flips to clockwise as it passes the magnet.

15 Quiz: 23-5 answer 15 The direction of the current in the ring is initially clockwise, and flips to counterclockwise as it passes the magnet. Lenz s law states: the direction of the induced current is such that the induced magnetic field opposes the change in the flux. The magnetic field due to the magnet goes from the north pole to the south pole. As the ring falls toward the magnet, the magnetic field through the ring is out of the page and increasing. The induced magnetic field points into the page to oppose the change. Using the right hand rule, you see that the current induced initially is clockwise. Once the ring passes the magnet, the magnetic field through the ring is out of the page and decreasing. The induced magnetic field points out of the page to oppose the change. So the current induced is counterclockwise.

16 Example: 1 16 The magnetic field shown in the figure decreases uniformly from B i = 1.0 T to B f = 0.4 T in Δt = 1.2 s. A loop with a radius r = 3.0 cm and a resistance R = Ω is perpendicular to the field. What is the size and direction of the current induced in the loop?

17 Example: 2 17 An emf is induced in a conducting loop of wire L = 1.22 m long as its shape is changed from square to circular. Find the average magnitude of induced emf if the change in shape occurs in Δt = 4.25 s and the local magnetic field, B = T, is perpendicular to the plane of the loop.

18 Applications of induced emf 18 Electric guitar pickup Dynamic microphone Magnetic tape recording

19 Magnetoencephalography (MEG) 19 MEG can measure the small current flowing in the human body using the weak magnetic field it produces. The change in magnetic field induces emfs in SQUIDs (superconducting quantum interference devices). In a MEG, the induced emfs are measured at many points just outside the cranium.

20 Quiz: 6 20 A wire loop is being pulled to the right through a uniform magnetic field that points into the page and suddenly ends. What is the direction of the induced current at the instance shown? A. Clockwise B. Counterclockwise C. No induced current 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 v

21 Quiz: 23-6 answer 21 Clockwise Lenz s law states: the direction of the induced current is such that the induced magnetic field opposes the change in the flux. The magnetic field within the loop points into the page, and the magnetic flux though the loop decreases as the loop moves to the right, exiting the magnetic field region. The induced magnetic field due to the induced current in the loop must point into the page: opposing the decreasing magnetic flux due to the external magnetic field into the page. Using the right hand rule, you see that the induced current flows clockwise. 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 v

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