Electromagnetic Induction and Faraday s Law

Transcription

1 Electromagnetic Induction and Faraday s Law

2 Solenoid

3 Magnetic Field of a Current Loop Solenoids produce a strong magnetic field by combining several loops. A solenoid is a long, helically wound coil of insulated wire. Chapter menu Resources Copyright by Holt, Rinehart and Winston. All rights reserved.

4 Recall Oersted s accidental discovery that current- carrying wire produces a magne9c field.

5 Soon a&er, Michael Faraday set out to explore whether a magne:c field could produce? an electric current

6 Induced emf intro giants5

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8 Induced EMF Almost 200 years ago, Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus:

9 Induced EMF He found no evidence when the current was steady, but did see a current induced when the switch was turned on or off.

10 Induced EMF Therefore, a changing magnetic field induces an emf. Faraday s experiment used a magnetic field that was changing because the current producing it was changing; the previous graphic shows a magnetic field that is changing because the magnet is moving.

11 Flux The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux: Unit of magnetic flux: weber, Wb. 1 Wb = 1 T m 2

12 Flux This drawing shows the variables in the flux equation:

13 Flux The magnetic flux is proportional to the total number of lines passing through the loop.

14 Faraday s Law of Induction; Lenz s Law Faraday s law of induction: [1 loop] [N loops]

15 MIT, emf & flux Lenz s Law

16 Faraday s Law of Induction; Lenz s Law Faraday s law of induction: [1 loop] [N loops]

17 Faraday s Law of Induction; Lenz s Law The minus sign gives the direction of the induced emf: A current produced by an induced emf moves in a direction so that the magnetic field it produces tends to restore the changed field.

18 MIT, Lenz

19 N (number of loops) MIT, Solenoid demo

20 How to Induce an EMF An emf can be induced whenever there is a change in flux. Since Φ B = BA cos θ an emf can be induced in three ways: 1. by a changing magnetic field B; 2. by changing the area of the loop in the field; 3. by changing the loop s orientation θ with respect to the field. 20

21 Case 1 I. Distance between coil and magnet decreases. So the magnetic field (therefore the flux) through the coil increases. III. Current is induced. II. To oppose this upward increase in the magnetic field (flux), the field produced by the induced current points downward. 21

22 How to Induce an EMF An emf can be induced whenever there is a change in flux. Since Φ B = BA cos θ an emf can be induced in three ways: 1. by a changing magnetic field B; 2. by changing the area of the loop in the field; 3. by changing the loop s orientation θ with respect to the field. 22

23 Case 2 Magnetic flux will change if the area of the loop changes:

24 Case 2 Area through the coil decreases Therefore A current can be induced by changing the area of the coil. Here, the induced current tries to maintain the original flux. 24

25 How to Induce an EMF An emf can be induced whenever there is a change in flux. Since Φ B = BA cos θ an emf can be induced in three ways: 1. by a changing magnetic field B; 2. by changing the area of the loop in the field; 3. by changing the loop s orientation θ with respect to the field. 25

26 Case 3 Magnetic flux will change if the angle between the loop and the field changes:

27 Case 3 Current in loop is induced clockwise to oppose decrease in flux as loop is rotated. 27

28 How to Induce an EMF An emf can be induced whenever there is a change in flux. Since Φ B = BA cos θ an emf can be induced in three ways: 1. by a changing magnetic field B; 2. by changing the area of the loop in the field; 3. by changing the loop s orientation θ with respect to the field. 28

29 Calculating the Magnitude of Flux

30 x x x x x x x x A x x x x x x x x n n θ n A = 40 cm 2 (a) θ = 0 0 (b) θ = 90 0 (c) θ = 60 0

31 Faraday s Law of Induction; Lenz s Law Problem Solving: Lenz s Law 1. Determine whether the magnetic flux is increasing, decreasing, or unchanged. 2. The magnetic field due to the induced current points in the opposite direction to the original field if the flux is increasing; in the same direction if it is decreasing; and is zero if the flux is not changing. 3. Use the right-hand rule to determine the direction of the current. 4. Remember that the external field and the field due to the induced current are different.

32 Faraday s Law: Rotating loop = B ΔA n n Loop at rest = A ΔB n

33 N = 200 turns B = 4 mt; 0 0 to 90 0 E = V

34 Induced B Induced B Left motion Right motion N S N S Flux increasing to left induces loop flux to the right. Flux decreasing by right move induces loop flux to the left.

35 Close switch. Then what is direction of induced current? R

36 Conceptual Example Practice with Lenz s law. In which direction is the current induced in the loop for each situation? 36

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