Lecture 11 th & 12 th week March April

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1 Lecture 11 th & 12 th week March April Chapter 14 Magnetism: Are you attracted or repelled? Where does magnetism come from? What use is magnetism? Post pictures and notes on refrigerators Electrical motors turn electricity into work Generators turn heat energy into electricity Transformers for power transmission and IPod. Earths Magnetic field. Northern lights. 1

2 Magnetism Electric charge is also responsible for the force that we call magnetism. Moving charge, that is a current, produces a force field which we term the magnetic field B. Since atoms contain moving charge most atoms and substances have magnetic behavior. In the case of iron this effect is very strong. 2

3 Magnetic field There are differences between the electric field and the magnetic field. A magnet has two poles and a magnetic monopole has never been observed. The field lines are continuous loops Like poles repel and unlike poles attract A magnetic field only acts on moving charge The force is perpendicular to the velocity so the moving charge is accelerated but does not gain or lose energy By definition the field lines enter a south pole and leave a north pole 3

4 Earth s magnetic field The earth has a dipole field inclined at 11 degrees to the axis of rotation. The North Pole (Arctic) is actually a magnetic south pole. It is thought that the field is produced by circulating electric currents in the molten iron core. 4

5 March Announcements for Exam 2 Help session for Exam 2 March Thursday 7:00-9:00pm Phys. Room 331 Exam 2 April Thursday 8:00-10:00 pm in Phys. Room 112 Exam Calculator: When taking a Physics 214 Exam, there is only one calculator model that is acceptable: The CASIO fx-260 SLRSC FRACTION. NO OTHER BRAND or TYPE WILL BE ALLOWED! 5

6 Form of the Magnetic force F moving charged particle F The force acting on a charged particle moving with velocity v in a magnetic field B is given by the vector product equation: F q v B F qvb sin This means the maximum force is when is at right angles to and that the force is zero if v is parallel to or v= 0. For a current in a wire qv = ql/t = IL so the force on a current carrying wire of length L is B B F IL B, F ILB sin Unit of B is Tesla = N / (coulombs/ sec meter) Newton / ( amper meter) v on a 6

7 6A-02 Weighing a Suspended Magnet Using equal and opposite forces between magnets to weigh magnet? Will the scale still balance when the second magnet floats? F magnetic F gravity F gravity F magnetic The scale will read the sum of forces acting on bottom magnet: F magnetic + F gravity The top magnet is floating so: F magnetic = F gravity The scale reads: F magnetic + F gravity = 2 F gravity = 2mg THE SECOND MAGNET S WEIGHT IS SENSED BY THE BALANCE EVEN THOUGH IT ISN T ACTUALLY TOUCHING THE APPARATUS. 7

8 6B-02 Force on a Moving Charge Investigating the behavior of moving charge in magnetic field Which orientation of the magnet causes the beam to move upward? Downward? B field v F q(v B) F q v Bsin Force MAGNETIC FIELD CAUSES THE CHARGED PARTICLES TO DEFLECT. WE FIND THE DIRECTION OF FORCE WITH THE RIGHT-HAND RULE. THIS IS THE FORCE ON POSITIVE CHARGE! 8

9 Fields from currents A current carrying wire produces circular field lines. Looking along the direction of the current the field lines are clockwise A current loop produces a dipole field which is identical to one which is produced by a short bar magnet. A solenoid can produce a strong uniform field in a volume with small leakage. If it is wound on an iron cylinder the field is stronger and more contained. This is an electromagnet. The magnetic field of an electromagnet is identical to a bar magnet of the same length and strength. 9

10 The magnetic force between two infinite current carrying wires If the two current carrying wires are very long then each wire sits in a B field which is at right angles to the wire. The force per unit length on either wire is: F/L = 2k I 1 I 2 /r L L k = 1 x 10-7 N/amp 2 The force exerted by one wire on the other is attractive when the currents are flowing in the same direction and repulsive when the currents are flowing in the opposite directions. 10

11 Force on a coil: Meters and Motors Ammeter consist of: coil of wire permanent C magnet restoring spring Direct current Motor consist of: wire wound into a loop mounted on an axel with a split ring and a battery. 11

12 Induction If a conductor is in a changing magnetic field an electromotive force is produced. If the conductor is part of a circuit then a current will flow. The induced current produces it s own magnetic field and the direction of the induced current produces a magnetic field that opposes the change. Self induction occurs when the current changes in a circuit for example when it is switched on or disconnected. The induced EMF slows down the change of current. anim0018.mov 12

13 6D-11 Jumping Ring Is there any differences in the two rings? Why one can jump up, the other can t? INDUCED CURRENT IN THE RING, CAUSED BY THE GROWING MAGNETIC FIELD WHEN THE SWITCH IS ACTIVATED, IS RESPONSIBLE FOR THE REPULSIVE FORCE BETWEEN THE COIL AND THE RING. IF A SPLIT RING IS PLACED OVER THE ELECTROMAGNET, THE COIL WILL NOT JUMP BECAUSE OF THE BROKEN CIRCUIT IN THE RING, PREVENTING THE CURRENT FLOW. 13

14 6D-09 Lenz s Law Two cylindrical objects, identical in appearance, are dropped successively through a long cylindrical aluminum tube. One objects drops freely whereas the other makes its way slowly through the tube. One of the cylinders is magnetized, setting up eddy currents that slow it down as it passes through the tube. 14

15 Magnetic Flux and the Principle of the Commercial Alternating Voltage (EMF= ) Generator In order to determine the induced EMF we have to define how the magnetic field changes as we rotate a conducting loop in a magnetic field. The important quantity is called magnetic flux and it is the scalar product of the magnetic field vector ( B) with the loop area vector ( A). B A B Acos, =B A perpendicular If we have a loop of N turns the induced EMF is: d N / t N ( Eq.1) dt A simple example: If we turn a N=50 loop coils around once, in t=1/20 second, we have N=50, d =BA, t=1/20. Thus Eq. 1 becomes ε = NΔ / t = 1000BA so if B was 1/10 tesla and A = 1/100 m 2 ε = 1 volt B Ф= BA 0 -BA Rotating a coil 15

16 General Derivation of the Alternating Voltage Generator Consider a conducting coil of area magnetic field B. A and N turns, inserted in A magnetic flux through the coil is: NAB NAB cos where is the angle between the loop area vector and magnetic field vectors. If the loop rotates in a fixed magnetic field around an axis, which is perpendicular to the magnetic field with an angular velocity, the time dependent flux through the coil is: ( t) NAB cos( t) The generated voltage EMF = is d dt NABs in t Eq.1 16 B

17 Eq. 1. is the principle of the commercial alternating - voltage generator dcos dt t ( Note that sin t ) If it is to be a conventional U.S. = 60Hz voltage generator then 2 Thus the amplitude V 0 of the generated sinusoidal voltage is: V NAB 2 NAB Eq 2 0. Hint: If you use the given units Hz, be given in units of volts. 2 m, Tesla your answer will 17

18 Transformers and generators The changing current in the primary produces changing magnetic flux in the secondary and an induced voltage. AC AC Ф Ф Naturally generates AC ΔV 2 / ΔV 1 = N 2 /N 1 can be step up or step down 18

19 Transmission In the distribution of electric power the goal is to deliver to the user as large a fraction as possible of the generated power. Practical cables have a specific resistance so the power losses will be I 2 R cable and we need I to be as small as possible. But we also need the delivered power P = V source I source to be as high as possible, therefore, the electrical power is distributed at very high voltage and low current. i V source R cable V user R user The voltage is reduced from 250,000volts to 220volts for households by using a transformer. The current increases by the same factor since for an ideal transformer no power is lost. Transformers are the dominant reason electrical transmission is alternating current i V user = V source IR cable P user = iv user = iv source i 2 R cable 19

20 Power Transmission: Generator Step up to 700 KeV Transmission Substation Step down to 1 KeV Home step down transformer to 220V Utilities (a) 110V (b) 220V The 110 volts are supplied by a ground wire and a 110V wires The 220 volt is supplied by the 110V wires 20

21 Household appliances Household circuits are wired in parallel so that when more than one appliance is plugged in each sees the same voltage and can get the required current. As we plug in more and more appliances the current in the circuit increases and the I 2 R losses could cause a fire. This is why we have fuses and why major appliances use 220 volts and many parts of the world use 220 volts for all household use. As many people turn on appliances (air conditioners) the grid has to supply more power by increasing the current. P user = iv user = iv source i 2 R cable This results in a higher fraction of the power being lost in the cable In cases of very heavy load the power station reduces the transmission voltage resulting in a brown out and in extreme cases there are rolling blackouts. 21

22 22

23 5B-11 Power Generator This demo utilizes a generator to turn mechanical energy into electricity and power various wattage lights. The apparatus consists of the generator and an array of 4 light sources: a 50 Watt incandescent bulb a 20 Watt Halogen bulb a 1.6 Watt LED array a large 6 Watt LED array The apparatus also includes an ammeter. 23

24 6B-16 Electric Generator This is a demonstration of an electric generator, an electromechanical device which converts mechanical energy to electrical energy. This model operates on the interaction of a conducting loop spinning in a magnetic field. A current is generated when the armature coil is forced to spin. 24

25 Summary of Chapter 14 Current produces a magnetic force field F = qv perp B moving charge F = ILB perp current Torque on a current loop - meters and motors F/L = 2k I 1 I 2 /r k = 1 x 10-7 N/amp 2 25

26 Induction Ф = B perpendicular A ε = NΔФ/t Transformer ΔV 2 / ΔV 1 = N 2 /N 1 Generator 26

27 Magnetic field of the earth The magnetic field is due to electrical currents in the molten core 27

28 Earth s magnetic field On Earth, the record of the reversal of the magnetic field is preserved in magnetic rocks which lie along the ocean floor. The magnetism preserved in these rocks points first in one direction, then in another direction. These rocks are lava flows or layers of microscopic sea creatures. The average time between reversals is ~ 250,000 years. The field traps charged particles in areas called the Van Allen belts. The field protects us from charged particles except at the poles 28

29 Questions Chapter 14 Q1 The north pole of a hand-held bar magnet is brought near the north pole of a second bar magnet lying on a table. How will the second magnet tend to move? It will be repelled Q4 Is it possible for bar magnet to have just one pole? The magnetic fields produced by currents require both a north and south poles. These poles do not exist as physical entities like an electron with one unit of charge. Physical laws do not prohibit the existence of monopoles, that is particles with magnetic charge, these have been searched for but never observed. 29

30 Q6 If we regard the earth as magnet, does its magnetic north pole coincide with its geographical north pole? What defines the position of the geographical north pole? The geographical north pole is defined by the axis of rotation. The magnetic north pole is determined by the currents and fields in the iron core of the earth. About every 250,000 years the field of the earth reverese. Q7 We visualized the magnetic field of the earth by imagining that there is a bar magnet inside the earth (fig. 14.7). Why did we draw this magnet with its south pole pointing north? The definition of the North pole is the point at which the North pole of a magnet would point. This means the North pole is a physical magnetic south pole. 30

31 Q9 A horizontal wire is oriented along an east-west line, and a compass is placed above it. Will the needle of the compass deflect when a current flows through the wire from east to west, and if so, in what direction? The current will produce a field that appears clockwise looking west. This means the compass will point north/south Q11 A uniform magnetic field is directed horizontally toward the north, and a positive charge is moving west through this field. Is there a magnetic force on this charge, and if so, in what direction? Point index finger along the velocity, the middle finger in the direction of B and then the thumb points in the direction of the force. The force points up. 31

32 Q12 A positively charged particle is momentarily at rest in a uniform magnetic field. Is there a magnetic force acting on this particle? No. The particle must have a velocity. Q13 If a uniform magnetic field is directed horizontally toward the east, and a negative charge is moving east through this field, is there a magnetic force on this charge, and if so, in what direction? No. There must be an angle between the velocity and the direction of B 32

33 Q15 If we look down at the top of a circular loop of wire whose plane is horizontal and that carries a current in the clockwise direction, what is the direction of the magnetic field at the center of the circle? The field is perpendicular to the plane in the direction that if you look in that direction the current is clockwise. So the answer is down. Q17 A current-carrying rectangular loop of wire is placed in an external magnetic field with the directions of the current and field as shown in the diagram. In what direction will this loop tend to rotate as a result of the magnetic torque exerted on it? B F B F 33

34 Q24 A horizontal loop of wire has a magnetic field passing upward through the plane of the loop. If this magnetic field increases with time, is the direction of the induced current clockwise or counterclockwise (viewed from above) as predicted by Lenz s law? The current induced produces a magnetic field that opposes the increase so the induced magnetic field points down so the current must be clockwise viewed from above. Q25 Two coils of wire are identical except that coil A has twice as many turns of wire as coil B. If a magnetic field increases with time at the same rate through both coils, which coil (if either) has the larger induced voltage? The flux in A is twice that in B so the induced voltage is twice as large. Q28 Does a simple generator produce a steady direct current? No. As the coil turns at constant angular velocity the rate of change of flux depends on the angle of the coil to the field so the current is AC 34

35 Q30 Can a transformer be used, as shown in the diagram below, to step up voltage of a battery? Explain. V 2 /V 1 = N 2 /N 1 So if N 2 > N 1 the voltage is stepped up. Q31 By stepping up the voltage of an alternating current source using a transformer, can we increase the amount of electrical energy drawn from the source? No. For an ideal transformer the input power = output power. In a real transformer energy is lost due to heat. Feel the transformer for your laptop. 35

36 Ch 14 E 4 Two parallel lines, each carrying I = 2amps, exert a force per unit length of 1.6 x 10-5 N/m on each other. What is distance between the lines? I = 2A F/l = (2k I 1 I 2 )/r r = (2k I 1 I 2 )/(F/l) = (2(1 x 10-7 )(2)(2))/(1.6 x 10-5 ) = 0.05 m I r I 36

37 Ch 14 E 8 Magnetic force on 40 cm straight wire segment carrying I = 5A is 2.5N. What is magnitude of magnetic field perpendicular to wire? F = IlB B = F/Il = (2.5)/(5)(0.40) = 1.25 T B I = 5A 0.40m 37

38 Ch 14 E 10 Loop of wire enclosing Area, A = 0.03m 2, has magnetic field passing thru its plane at an angle. Component of magnetic field perpendicular to plane = 0.4T, while component parallel to plane = 0.6T. What is magnetic flux thru coil? I = B 1 A = 0.4(0.03) = 0.012Tm 2 A 38

39 Ch 14 E 12 Coil of wire with 60 turns and cross-sectional area, A = 0.02m 2, lies with it s plane perpendicular to B = 1.5T magnetic field. Coil is rapidly removed B-field in time t=0.2s. a) What is initial magnetic flux thru coil? b) What is average voltage induced in coil? a) Φ = NB 1 A = (60)(1.5)(0.02) = 1.8Tm 2 b) ε = ΔΦ/t = (1.8 Tm 2 0)/0.2s = 9V 39

40 Ch 14 CP 2 Small metal ball has charge q = +0.05C and mass, m = 0.025kg. Ball enters a region of magnetic field B = 0.5 T that is perpendicular to its velocity v = 200m/s. a) What is magnitude of magnetic force on ball? b) What is direction of magnetic force on ball? c) Will this force change magnitude of ball s velocity? d) Use Newton s 2 nd Law, what is magnitude of acceleration of the ball? e) Centripetal acceleration = v 2 /r. What is radius of the curve ball will move thru in magnetic field? 40

41 v vyˆ ẑ ˆx B Bxˆ ŷ Ch 14 CP 2 (cont) a) F = qv 1 B = (0.05)(200)(0.5) = 5N b) (see diagram) Force in z direction c) To change magnitude of velocity is to change kinetic energy. If magnetic field changes kinetic energy then it must do work on charged ball. The right-hand rule shows us that velocity and force are always perpendicular. Therefore, the magnetic field can do no work! d) F = ma = qv 1 B = 5N a = 5N/0.025kg = 200 m/s 2 e) v 2 /r = 200m/s 2, r = v 2 /(200m/s 2 ) = (200m/s) 2 /200m/s 2 = 200m 41

42 Ch 14 CP 4 Transformer is designed to step down line voltage of 110V to 22V. Primary coil has 400 turns of wire. a) How many turns of wire on secondary coil? b) Current in primary I 1 = 5A. What is max current in second coil? c) If transformer gets warm during operation, will current in secondary coil equal that computed in previous question (b)? a) ΔV 2 / ΔV 1 = N 2 /N 1, N 2 = N 1 (ΔV 2 / ΔV 1 ) = 400(22/110) = 80 turns b) ΔV 2 I 2 ΔV 1 I 1 I 1 = 110/22 (5) = 25A Max current in second coil = 25A. c) No, heat that warms up transformer is power dissipated in the form P = I 2 R. Power is lost to heat. 42

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