Slide 1 / 50. Slide 2 / 50. Slide 3 / 50. Electromagnetic Induction and Faraday s Law. Electromagnetic Induction and Faraday s Law.

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1 Electromagnetic Induction and Faraday s Law Slide 1 / 50 Electromagnetic Induction and Faraday s Law Slide 2 / 50 Induced EMF Faraday s Law of Induction Lenz s Law EMF Induced in a Moving Conductor Changing Magnetic Flux Produces an Electric Field Induced EMF Slide 3 / 50 Almost 200 years ago, Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus:

2 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. Slide 4 / 50 Faraday s Law of Induction; Lenz s Law Slide 5 / 50 The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux is defined by: F B = B^A Unit of magnetic flux: weber, Wb. 1 Wb = 1 T m 2 F is the Greek letter "phi" and stands for "flux", or flow. F B represents magnetic flux, or the flow of magnetic field through a surface. 1 What is the flux through a loop of wire if a magnetic field of 0.40 T is perpendicular to it and its area is 5.0 m 2? (always use 2 significant figures) Slide 6 / 50 F B = B^A

3 2 What is the flux through a loop of wire if a magnetic field of 0.30 T is perpendicular to it and its radius is 2.0 m? (always use 2 significant figures) F B = B^A Slide 7 / 50 In the below diagram, the magnetic field (blue) is perpendicular to the plane of the loop of wire (orange) and parallel to its normal (red) so the flux is just given by # B= BA. Slide 8 / 50 If the flux passes directly though the loop of wire, perpendicular to it, then it is a maximum and # B= BA. In this case, the magnetic field (blue) is parallel to the plane of the loop of wire (orange) and perpendicular to its normal, so the flux is just given by # B = 0. Slide 9 / 50 If the magnetic field lines don't go through the loop of wire, there is no flux.

4 Faraday s Law of Induction; Lenz s Law Slide 10 / 50 The magnetic flux is is proportional to the total number of lines passing through the loop. 3 What is the magnitude of the magnetic flux through the loop of wire shown below. The magnetic field is 1.0 T and the area of the loop of wire is 5.0 m 2. Slide 11 / 50 4 What is the magnitude of the magnetic flux through the loop of wire shown below. The magnetic field is 1.0 T and the area of the loop of wire is 5.0 m 2. Slide 12 / 50

5 Faraday s Law of Induction; Lenz s Law Slide 13 / 50 Faraday s law of induction: E is the induced emf (electromovtive force) and is measured in volts (V) N is the number of loops of wire in the coil D# Bo represents the change in the magnetic flux and is measured in Webers (Wb) is the time interval during which the flux changed and is measured in seconds (s) the "-" sign has to do with the direction of the emf, and will be discussed later Faraday s Law of Induction; Lenz s Law Slide 14 / 50 The minus sign tells us the direction of the induced EMF. Let's get back to that a little later, for right now let's determine the magnitude of the induced EMF. For instance, let's figure out the induced emf in a 8.0 m 2 coil if it is in a perpendicular 0.40T magnetic field that disappears over a time interval of 2.0s? (Let's assume there's just a single loop of wire.) What is the induced emf in a 8.0 m 2 coil (consisting of one loop) if it is perpendicular to a 0.40T magnetic field that disappears over a time interval of 2.0s? N = 1 A = 8.0 m 2 B 0 = 0.4T # Bo = B 0 A = (0.4T)(8.0 m 2 ) = 3.2W B f = 0 # Bf = B 0 A = (0)(8.0 m 2 ) = 0 = 2.0s Slide 15 / 50 D# E = -N B (# Bf - # Bo) E = -N (0-3.2Wb) E = -1 = 1.6V Alternatively s

6 What is the induced emf in a 8.0 m 2 coil (consisting of one loop) if it is perpendicular to a 0.40T magnetic field that disappears over a time interval of 2.0s? Slide 16 / 50 N = 1 A = 8.0 m 2 B 0 = 0.4T B f = 0 = 2.0s D# E = -N B DBA E = -N E = -NA DB B E = -NA f-b 0 E = -1(8.0 m 2 (0-0.40T) ) = 1.6V 2.0s The second approach works because anything that is not changing can be put in front of the delta symbol. For instance, if A is constant while B is changing: Slide 17 / 50 D# E = -N B D(BA) E = -N (BA) f - (BA) 0 E = -N (B fa f) - (B 0A 0) E = -N (B fa) - (B 0A) E = -N A(B f - B 0) E = -N In this case A f = A 0 = A this becomes: Since A is in both terms, it can be factored out But [B f - B 0] is just DB DB E = -NA The same approach allows me to factor out B if it is not changing while A is changing 5 What is the magnitude of the induced emf in a single loop 2.0m 2 coil if it is perpendicular to a 0.50T magnetic field which is turned off over a time interval of 4.0s? Slide 18 / 50

7 6 What is the magnitude of the induced emf in a ten loop coil of wire whose area is 2.0m 2 if it is perpendicular to a magnetic field which is increased from 0.30T to 1.5T over a time interval of 4.0s? Slide 19 / 50 Faraday s Law of Induction; Lenz s Law Slide 20 / 50 Magnetic flux will change if the area of the loop changes: Faraday s Law of Induction; Lenz s Law Slide 21 / 50 Magnetic flux will change if the angle between the loop and the field changes:

8 7 A 4.0m2 single loop coil of wire is initially perpendicular to a 0.60T magnetic field. It is then rotated so that it become parallel to that magnetic field 2.0s later. What is the magnitude of the induced emf? Slide 22 / 50 8 A coil of wire, consisting of 50 loops, is perpendicular to a 1.2T magnetic field. The area of the coil is increased from 0.40m 2 to 1.2m 2 over a time of 5.0s. What is the magnitude of the induced emf in the coil? Slide 23 / 50 Lenz s Law Slide 24 / 50 The minus sign tells us that the direction of the induced emf is such that the resulting current produces a magnetic field that resists the change of flux through the loop. For instance, if the external field gets weaker, the current tries to replace the "missing" external field. If the external field gets stronger, the induced current tries to opposes the "extra" external field. Only worry about the field within the loop, ignore the field outside it.

9 Lenz s Law Slide 25 / 50 Initial External Field (red).... Final External Field (red) Plus Field due to Induced Current (blue).... The current flows CCW to create a field out of the board (dots) to oppose the change in the external field Lenz s Law Slide 26 / 50 Initial External Field (red) Final External Field (red).... Plus Field due to Induced Current (blue) x x x x. x x. x. x. x. x. x. x. x. x. x. x. x x x x The current flows CW to create a field into the board (blue "x"s) to cancel the new external field (red dots) Lenz s Law Slide 27 / 50 Initial External Field (red) x x x x x x x x x x x x x x x x x x x x Final External Field (red).... Plus Field due to Induced Current (blue) 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. x x x x x x x x x The current flows CW to create a field into the board (blue "x"s) to cancel the new external field (red dots) and replace the old external field (red "x"s)

10 Faraday s Law of Induction; Lenz s Law Slide 28 / 50 Problem Solving: Lenz s Law Determine whether the magnetic flux is increasing, decreasing, or unchanged. 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. Use the right-hand rule to determine the direction of the current. Remember that the external field and the field due to the induced current are different. 9 A magnetic field is pointing straight up through a coil of wire. The field is suddenly turned off. What is the direction of the induced current in the wire? Slide 29 / 50 A B C D E Out of the page Into the page Clockwise Counterclockwise There is no induced current 10 A magnetic field is pointing straight up through a coil of wire. The field is suddenly doubled in magnitude. What is the direction of the induced current in the wire? Slide 30 / 50 A B C D E Out of the page Into the page Clockwise Counterclockwise There is no induced current

11 11 A coil of wire is sitting on a table top. A magnet is held above it with it's north pole pointed downwards. What is the direction of the induced current? Slide 31 / 50 A B C D E Out of the page Into the page Clockwise Counterclockwise There is no induced current 12 A coil of wire is sitting on a table top. A magnet is held above it with it's north pole pointed downwards. The magnet is released and falls towards the coil. What is the direction of the induced current? Slide 32 / 50 A B C D E Out of the page Into the page Clockwise Counterclockwise There is no induced current EMF Induced in a Moving Conductor Slide 33 / 50 This image shows another way the magnetic flux can change:

12 EMF Induced in a Moving Conductor Slide 34 / 50 The induced current is in a direction that tends to slow the moving bar it will take an external force to keep it moving. EMF Induced in a Moving Conductor The induced emf has magnitude Slide 35 / 50 EMF Induced in a Moving Conductor Slide 36 / 50 Another perspective Magnetic Force Electric Force SF = ma F B - F E = 0 qvb - qe = 0 vb = E but E = V/d vb = V/d V/d = vb V is E E = Blv but d is just l and

13 13 What is the voltage between the ends of a 100m long metal rod which is traveling at a velocity of 400 m/s perpendicularly through a 5 x 10-4 T magnetic field? Slide 37 / 50 Changing Magnetic Flux Produces an Electric Field Slide 38 / 50 A changing magnetic flux induces an electric field; this is a generalization of Faraday s law. The electric field will exist regardless of whether there are any conductors around. Electric Generators A generator is the opposite of a motor it transforms mechanical energy into electrical energy. This is an ac generator: Slide 39 / 50 The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings.

14 Electric Generators Slide 40 / 50 A dc generator is similar, except that it has a split-ring commutator instead of slip rings. Transformers and Transmission of Power Slide 41 / 50 A transformer consists of two coils, either interwoven or linked by an iron core. A changing emf in one induces an emf in the other. The ratio of the emfs is equal to the ratio of the number of turns in each coil: Transformers and Transmission of Power Slide 42 / 50 This is a step-up transformer the emf in the secondary coil is larger than the emf in the primary:

15 Transformers and Transmission of Power Slide 43 / 50 Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio of turns: P in = P out I in V in = I out V out I primary V primary = I secondary V secondary I secondary V primary = I primary V secondary I secondary N primary = I primary N secondary Transformers and Transmission of Power Slide 44 / 50 Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac. Applications of Induction: Sound Systems, Computer Memory, Seismograph, GFCI Slide 45 / 50 This microphone works by induction; the vibrating membrane induces an emf in the coil

16 Applications of Induction: Sound Systems, Computer Memory, Seismograph, GFCI Slide 46 / 50 Differently magnetized areas on an audio tape or disk induce signals in the read/write heads Applications of Induction: Sound Systems, Computer Memory, Seismograph, GFCI Slide 47 / 50 A seismograph has a fixed coil and a magnet hung on a spring (or vice versa), and records the current induced when the earth shakes. Applications of Induction: Sound Systems, Computer Memory, Seismograph, GFCI Slide 48 / 50 A ground fault circuit interrupter (GFCI) will interrupt the current to a circuit that has shorted out in a very short time, preventing electrocution.

17 Summary of Chapter 21 Slide 49 / 50 Magnetic flux: Changing magnetic flux induces emf: Induced emf produces current that opposes original flux change Changing magnetic field produces an electric field Slide 50 / 50