1 Electromagnetic Induction Taking It To The Maxwell

2 Michael Faraday (1791 – 1867)

3 Introduction We’ve discussed two ways in which electricity and magnetism are related: (1) an electric current produces a magnetic field. (2) a magnetic field exerts a force on an current carrying wire or moving electric charge.

4 Introduction These discoveries were made in 1820 – Scientists wondered: If electric currents produce a magnetic field, does a magnetic field produce electric currents? Joseph Henry (1797 – 1878) and Michael Faraday (1791 – 1867) independently found, ten years later, that this is so.

5 Hey Mikey! Faraday found that Faraday found that changing a magnetic field produces a current. Such a current is called an. Such a current is called an induced current. To move charges requires a force and this force is Called the ELECTROMAGNETIC FORCE, for short. EMF for short. You know it as VOLTS of potential.

6 Mikey found that a steady current in X produced no current in Y. Only when the current in X was starting or stopping (i.e., changing) was a current produced in Y. Faraday suspected that a magnetic field would induce a current, just like a current produces a magnet field. Induced Current

7 The Big Idea To induce a current in a wire …. The MAGNETIC FIELD MUST BE CHANGING WITH RESPECT TO TIME There are a number of differential equations to describe this, but why complicate things?

8 Since there is no change in the magnetic flux, no current is induced.

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

10 III. Current is induced in the opposite direction as the previous case. I. Distance between magnet and coil increases. So the magnetic field (and therefore the flux) decreases. II. To oppose the decrease in the upward magnetic field (flux), the induced current produces an upward magnetic field, trying to maintain the “status quo.”

11 The Big Idea! The induced current moves such that its magnetic field tends to oppose and resist the bar magnet’s moving field. Essentially it wants to DAMPEN the other field. Nature wants the two fields to be in harmony. This is LENZ’S LAW and it explains why the magnet falls slowly through the copper pipe!

12 Lenz’s Law An induced emf always gives rise to a current whose magnetic field opposes the original change in flux. An induced emf is always in a direction that opposes the original change in flux that caused it.

13 The Flux Capacitor The measure of how the field changes has to do with an amount, or area, of coil or loop of wire exposed to the field. It doesn’t matter if the field is in motion, changing in intensity, or if the coil is moving. So long as – FROM THE POINT OF VIEW OF THE WIRE - the B field appears to be changing with respect to time.

14 The Flux Capacitor Magnetic flux is a measure of field strength B over an area measured in m 2. Think of it this way. The absolute amount of rain fall is 2” per hour over the entire state. We only care about a small part, namely a square foot.

15 The Flux Capacitor

16 Phi, Fi, Pho, Phum? The unit of flux is the Henry, named for Joseph Henry. The symbol is the capitol Greek letter Phi…. Φ = B X A Φ = B A cosθ Henry = Tesla m 2

17 Case 1 Motion I A current can be induced by changing the area of the field exposed to the coil. Here the area depends on moving the coil into the field.

18 A current can be induced by changing the area of the coil exposed to the field by collapsing the coil. Here, the area is changed by shrinking the ring. Area through the coil decreases Therefore Case 2

19 A current can be induced by changing the area of the coil exposed to the field. Here, the area is changed by rotating with respect to the field. I This side is coming toward you Case 3 – A Generator

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

21 Fleming’s LHR Revisited

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23 I Area has increased

24 dx =

25 I F

26 Umm….Sorry But we simply have to have a differential equation. Emf = change in Flux = B Field x Change in Area change in time change in time change in time change in time Emf = B Field x length x velocity x change in time change in time change in time

27 EMF Induced in a Moving Conductor  = = = = Blv d  B B dA Blv dt dt dt dt This equation is valid as long as B, l, and v are mutually perpendicular.

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29 Rotating clockwise F = qv x B is the force on the charges in the wire that produces a current.

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33 Faraday’s Law of Induction  = N dBdB Faraday found, experimentally, that the magnitude of the induced emf is proportional to the: rate of change of magnetic flux. dt N = Number of loops of wire Lenz’s law Induced emf

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44 Example 29-5 An ac generator. The armature of a 60-Hz ac generator rotates in a 0.15-T magnetic field. If the area of the coil is 2.0 x m 2, how many loops must the coil contain if the peak output is to be  0 = 170 V?

45 DC Generator A dc generator is much like an ac generator or alternator, except the slip rings are replaced by split-ring commutators, just as in a dc motor.

Transformers and the Transmission of Power A transformer is a device for increasing or decreasing an ac voltage. A transformer is a device for increasing or decreasing an ac voltage. It consists of two coils of wire known as the primary and secondary coils. It consists of two coils of wire known as the primary and secondary coils.

Transformers and the Transmission of Power A transformer is a device for increasing or decreasing an ac voltage. A transformer is a device for increasing or decreasing an ac voltage. A transformer may be a step-up transformer (increasing voltage) or a step-down transformer (decreasing voltage). A transformer may be a step-up transformer (increasing voltage) or a step-down transformer (decreasing voltage). A transformer consists of two coils of wire known as primary (voltage input) and secondary (voltage output) coils. A transformer consists of two coils of wire known as primary (voltage input) and secondary (voltage output) coils.= VSVPVSVP NSNPNSNP Transformer equation:

48 Example 29-8 Portable radio transformer. A transformer for home use of a portable radio reduces 120-V ac to 9.0-V ac. The secondary contains 30 turns and the radio draws 400 mA. Calculate (a) the number of turns in the primary; (b) the current in the primary; and (c) the power transformed.

49 Example 29-9 Transmission lines. An average of 120 kW of electric power is sent to a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 . Calculate the power loss if the power is transmitted at (a) 240 V and (b) 24,000 V.

Changing Magnetic Flux Produces an Electric Field A changing magnetic flux induces an emf and a current in a conducting loop. Therefore, it produces an electric field.

51 Changing Magnetic Flux Produces an Electric Field Changing magnetic flux induces current-emf- electric field. Changing magnetic flux induces current-emf- electric field. An electric field is always generated by a changing magnetic flux, even in free space where no charges are present An electric field is always generated by a changing magnetic flux, even in free space where no charges are present Flux-induced field has properties different from electrostatic electric field produced by stationary charges. Flux-induced field has properties different from electrostatic electric field produced by stationary charges.

52 Faraday’s Law – General Form E dl = E dl = d  B dt

53 Forces Due to Changing B are Nonconservative An electric field is induced by a changing magnetic field, even in the absence of a conductor. An electric field is induced by a changing magnetic field, even in the absence of a conductor. The induced electric field E that appears in the in the previous equation, is a nonconservative, time-varying field produced by a changing magnetic field. The induced electric field E that appears in the in the previous equation, is a nonconservative, time-varying field produced by a changing magnetic field. Electric field lines produced by static charges stop and end on charges. Electric field lines produced by static charges stop and end on charges. Electric field lines produced by a changing magnetic field are continuous; they form closed loops. Electric field lines produced by a changing magnetic field are continuous; they form closed loops.

54 Electrostatic E Field

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57 Forces Due to Changing B are Nonconservative The fact that the integral of E dl around a closed path is zero follows from the fact that electro static force is a conservative force, and so a potential energy function could be defined. The fact that the integral of E dl around a closed path is zero follows from the fact that electro static force is a conservative force, and so a potential energy function could be defined. The above tells us that the work done per unit charge around any closed path is zero. The above tells us that the work done per unit charge around any closed path is zero. That is the work done between any two points is independent of the path, which is a property of a conservative force. That is the work done between any two points is independent of the path, which is a property of a conservative force.

58 Forces Due to Changing B are Nonconservative But the generalized form of Faraday’s law tells us that the integral around a closed path is not zero. But the generalized form of Faraday’s law tells us that the integral around a closed path is not zero. Thus we are unable to define a potential energy function. Thus we are unable to define a potential energy function. Thus we conclude that when the electric force is produced by a changing magnetic field the forces are not conservative. Thus we conclude that when the electric force is produced by a changing magnetic field the forces are not conservative.

59 Example E produced by changing B. A magnetic filed B between the pole faces of an electromagnetic is nearly uniform at any instance over a circular area of radius r 0. The current in the windings of the electromagnet is increasing in time so that B changes in time at a constant rate dB/dt at each point. Beyond the circular region (r > r 0 ), we assume B = 0 at all times. Determine the electric field E at any point P a distance r from the center of the circular area.

60 Changing Magnetic Flux Produces an Electric Field Electrons in the moving conductor must feel a force since there is a current. Electrons in the moving conductor must feel a force since there is a current. A force implies that there is an electric field in the conductor. A force implies that there is an electric field in the conductor. Therefore, we conclude that a changing magnetic flux produces an electric field. Therefore, we conclude that a changing magnetic flux produces an electric field. E = = = vB F qvB q

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66 I FBFB F ext = ?

67 I FBFB F ext = ?