PHY 1214 General Physics II

Transcription

1 PHY 1214 General Physics II Lecture 19 Induced EMF and Motional EMF July 5-6, 2005 Weldon J. Wilson Professor of Physics & Engineering Howell Hall 221H

2 Lecture Schedule (Weeks 4-6) We are here. July 5, 2005 PHY Lecture 19 2

3 The History of Induction In 1831, Joseph Henry, a Professor of Mathematics and Natural Philosophy at the Albany Academy in New York, discovered magnetic induction. In July, 1832 he published a paper entitled On the Production of Currents and Sparks of Electricity from Magnetism describing his work. Because Henry published after Michael Faraday, his did not receive much credit for this discovery, which actually preceded Faraday s. Michael Faraday's ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a magnetic field should be able to produce an electric current. He demonstrated this principle of induction in 1831 and published his results immediately. The principle of induction was a landmark in applied science, for it made possible the dynamo, or generator, which produces electricity by mechanical means. Joseph Henry ( ) Michael Faraday ( ) July 5, 2005 PHY Lecture 19 3

4 Faraday s Discovery Faraday had wound two coils around the same iron ring. He was using a current flow in one coil to produce a magnetic field in the ring, and he hoped that this field would produce a current in the other coil. Like all previous attempts to use a static magnetic field to produce a current, his attempt failed to generate a current. However, Faraday noticed something strange. In the instant when he closed the switch to start the current flow in the left circuit, the current meter in the right circuit jumped ever so slightly. When he broke the circuit by opening the switch, the meter also jumped, but in the opposite direction. The effect occurred when the current was stopping or starting, but not when the current was steady. Faraday has invented the picture of lines of force, and he used this to conclude that the current flowed only when lines of force cut through the coil. July 5, 2005 PHY Lecture 19 4

5 Faraday Investigates Induction Faraday placed one coil above the other, without the iron ring. Again there was a momentary current when the switch opened or closed. Faraday replaced the upper coil with a bar magnet. He found that there was a momentary current when the bar magnet was moved in or out of the coil. Conclusion: There is a current in the coil if and only if the magnetic field passing through the coil is changing. Was it necessary to move the magnet? Faraday placed the coil in the field of a permanent magnet. He found that there was a momentary current when the coil was moved. July 5, 2005 PHY Lecture 19 5

6 Motional EMF Consider a length l of conductor moving to the right in a magnetic field that is into the diagram. Positive charges in the conductor will experience an upward force and negative charges a downward force. The net result is that charges will pile up at the two ends of the conductor and create an electric field E. When the force produced by E becomes large enough to balance the magnetic force, the movement of charges will stop and the system will be in equilibrium. FB = qvb FE = qe FB = FE E = vb July 5, 2005 PHY Lecture 19 6

7 Separating Charge E = V x V = E x = E l but E = vb, so V = vlb V = E x (Magnitude only) ε = vlb July 5, 2005 PHY Lecture 19 7

8 Question 1 The square conductor moves upward through a uniform magnetic field that is directed out of the diagram. Which of the figures shows the correct distribution of charges on the conductor? July 5, 2005 PHY Lecture 19 8

9 Example: A Battery Substitute A 6.0 cm long flashlight battery has an EMF of 1.5 V. With what speed must a 6.0 cm wire move through a 0.10 T magnetic field to create the same EMF? ε = vlb v ε = lb = ( 1.5 V) ( 0.06 m)( 0.10 T) = 250 m/s July 5, 2005 PHY Lecture 19 9

10 Induced Current in a Circuit The figure shows a conducting wire sliding with speed v along a U-shaped conducting rail. The induced emf E will create a current I around the loop. ε = vlb ε I = = R vlb R July 5, 2005 PHY Lecture 19 10

11 Question 2 Consider the system shown in the figure. Which description of the induced current is correct? (a) There is a clockwise current; (b) There is a counterclockwise current; (c) There is no current; July 5, 2005 PHY Lecture 19 11

12 Force and Induction We have assumed that the sliding conductor moves with a constant speed v. It turns out that a current carrying wire in a magnetic field experiences a force F mag, so we must supply a counter-force F pull to make this happen. vlb Fpull = Fmag = IlB = lb = R vl B R 2 2 July 5, 2005 PHY Lecture 19 12

13 Energy Considerations P = F v = pull pull v l B R vlb v l B Pdissipated = I R = R = R R Therefore, the work done in moving the conductor is equal to the energy dissipated in the resistance. Energy is conserved. Whether the wire is moved to the right or to the left, a force opposing the motion is observed. July 5, 2005 PHY Lecture 19 13

14 Example: Lighting A Bulb The figure shows a circuit including a 3 V 1.5 W light bulb connected by ideal wires with no resistance. The right wire is pulled with constant speed v through a perpendicular 0.10 T magnetic field. (a) What speed must the wire have to light the bulb to full brightness? (b) What force is needed to keep the wire moving? v = E (3.0 V) 300 m/s lb = (0.10 m)(0.10 T) = I (3.0 V) R = = = 6.0 Ω V (0.50 A) I P (1.5 W) = = = 0.50 A V (3.0 V) F pull vl B = = R (300 m/s)(0.10 m) (0.10 T) (6.0 Ω) N = July 5, 2005 PHY Lecture 19 14

15 Eddy Currents Suppose that a rigid square copper loop is between the poles of a magnet. If the loop moves, as long as no conductors are in the field of the magnet there will be no current and no forces. But when one side of the loop enters the magnetic field, a current flow will be induced and a force will be produced. Therefore, a force will be required to pull the loop out of the magnetic field, even though copper is not a magnetic material. However, if we cut the loop, there will be no force. July 5, 2005 PHY Lecture 19 15

16 Eddy Currents (2) Another way of looking at the system is to consider the magnetic field produced by the current in the loop. The current loop is effectively a dipole magnet with a S pole near the N pole of the magnet, and vice versa. The attractive forces between these poles must be overcome by an external force to pull the loop out of the magnet. July 5, 2005 PHY Lecture 19 16

17 Eddy Currents (3) Now consider a sheet of conductor pulled through a magnetic field. There will be induced current, just as with the wire, but there are now no welldefined current paths. As a consequence, two whirlpools of current will circulate in the conductor. These are called eddy currents. A magnetic braking system. July 5, 2005 PHY Lecture 19 17

18 Question 3 What is the ranking of the forces in the figure? (a) F 1 =F 2 =F 3 =F 4 ; (b) F 1 <F 2 =F 3 >F 4 ; (c) F 1 =F 3 <F 2 =F 4 ; (d) F 1 =F 4 <F 2 =F 3 ; (e) F 1 <F 2 <F 3 =F 4 ; July 5, 2005 PHY Lecture 19 18

19 End of Lecture 19 Before the next lecture, read Sections 22.1 through July 5, 2005 PHY Lecture 19 19