This Week 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. 1/22/2018 Physics 214 Summer 2018 1
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. 1/22/2018 Physics 214 Summer 2018 2
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 http://www.physics.purdue.edu/class/applets/phe/mfbar.htm 1/22/2018 Physics 214 Summer 2018 3
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. 1/22/2018 Physics 214 Summer 2018 4
Form of the force The force a charged particle moving with velocity v in a magnetic field B is given by F = qv perpendicular B or F = qvb perpendicular This means the maximum force is when v is at right angles to B and that the force is zero if v is parallel to B 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 F = ILB perp Units of B are tesla (N x sec/coulombs x meters) (N/amps.meters) http://www.physics.purdue.edu/class/applets/phe/lorentzforce.htm 1/22/2018 Physics 214 Summer 2018 5
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. 1/22/2018 Physics 214 Summer 2018 6
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? Force F = q (v B) 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! 1/22/2018 Physics 214 Summer 2018 7
Fields from currents A current carrying wire produces circular field lines. Looking along the direction of the current the field lines are clockwise http://www.physics.purdue.edu/class/applets/phe/mfwire.htm A current loop produces a dipole field A solenoid can produce a strong uniform field in a volume with small leakage. If it is placed in an iron cylinder the field is stronger and more contained 1/22/2018 Physics 214 Summer 2018 8
Force between two infinite wires If the two wires are very long then each wire sits in a B field which is at right angles to the wire. F/L = 2k I 1 I 2 /r k = 1 x 10-7 N/amp 2 1/22/2018 Physics 214 Summer 2018 9
Force on a coil: Meters and Motors http://www.physics.purdue.edu/class/applets/phe/electricmotor.htm 1/22/2018 Physics 214 Summer 2018 10
Moving conductor B Suppose a wire is moving with velocity v in a magnetic field so that v is into the screen. Positive charge will feel a force to the right. If the wire is isolated then an electromotive force will exist between the ends of the wire and if the wire is part of a circuit this electromotive force will cause a current to flow. The electrical energy is produced by the force that is moving the wire and the wire requires a force to keep it moving at constant velocity ε F 1/22/2018 Physics 214 Summer 2018 11
6B-06 Magnetic Force on a Current-Carrying Conductor Finding the direction of Force on Current due to B-field Based on the direction of the Magnetic Field and the direction that current flows, can you predict in which direction the Force points? B I F F/L = I B Use right-hand rule to find direction of F CURRENT FLOWING ALONG THE AXLE IS PERPENDICULAR TO THE MAGNETIC FIELD. THERE IS A FORCE ON THE AXLE, CAUSING IT TO ROLL. IF THE CURRENT IS REVERSED, THE AXLE ROLLS IN THE OPPOSITE DIRECTION. 1/22/2018 Physics 214 Summer 2018 12
6B-11 Force Between Coil and Wire Forces between two conductors What occurs when the current is sent through? How about reversing the current? What differences occur in the interacting fields if one of the wires is replaced by a solenoid? WHEN THE SOLENOID IS ACTIVATED AND A CURRENT IS SENT THROUGH THE WIRE, THE WIRE WRAPS ITSELF AROUND THE SOLENOID. WHEN THE CURRENT IN THE WIRE IS REVERSED, IT WRAPS AROUND THE SOLENOID IN THE OPPOSITE DIRECTION. 1/22/2018 Physics 214 Summer 2018 13
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 1/22/2018 Physics 214 Summer 2018 14
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. 1/22/2018 Physics 214 Summer 2018 15
Magnetic flux In order to determine the induced EMF we have to define how the magnetic field changes as we move a conductor through a magnetic field. The important quantity is called magnetic flux and it is a product of the magnetic field perpendicular to the loop times the area Ф = B perpendicular A If we have a loop of N turns ε = N Ф/t So if we turn 50 loops in 1/20 second ε = Ф/t = 1000BA so if B was 1/10 tesla and A = 1/100 m 2 ε = 1 volt 1/22/2018 Physics 214 Summer 2018 16 B Ф= BA 0 -BA Rotating a coil
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 V 2 / V 1 =N 2 /N 1 can be step up or step down http://www.physics.purdue.edu/class/applets/phe/generator_e.htm 1/22/2018 Physics 214 Summer 2018 17
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 1/22/2018 Physics 214 Summer 2018 18
Induction Ф = B perpendicular A ε = N Ф/t Transformer V 2 / V 1 =N 2 /N 1 Generator 1/22/2018 Physics 214 Summer 2018 19
Our World 1/22/2018 Physics 214 Summer 2018 20
Magnetic field of the earth The magnetic field is due to electrical currents in the molten core 1/22/2018 Physics 214 Summer 2018 21
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 1/22/2018 Physics 214 Summer 2018 22
Worked Questions and Problems 1/22/2018 Physics 214 Summer 2018 23
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. 1/22/2018 Physics 214 Summer 2018 24
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. 1/22/2018 Physics 214 Summer 2018 25
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. 1/22/2018 Physics 214 Summer 2018 26
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 1/22/2018 Physics 214 Summer 2018 27
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 1/22/2018 Physics 214 Summer 2018 28
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 1/22/2018 Physics 214 Summer 2018 29
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. 1/22/2018 Physics 214 Summer 2018 30
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 1/22/2018 Physics 214 Summer 2018 31
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 1/22/2018 Physics 214 Summer 2018 32
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) A = 0.012Tm 2 1/22/2018 Physics 214 Summer 2018 33
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 1/22/2018 Physics 214 Summer 2018 34
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? 1/22/2018 Physics 214 Summer 2018 35
Ch 14 CP 2 (cont) ẑ v vyˆ ˆx........ B Bxˆ ŷ 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 1/22/2018 Physics 214 Summer 2018 36
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. 1/22/2018 Physics 214 Summer 2018 37
Waves In our everyday life there are many examples of waves for example, Sound, ocean waves, strings of musical instruments, organ pipes These are examples of waves which need a medium to travel through and the general definition of such waves is A disturbance which propagates through a medium but the medium itself only moves locally as the wave passes. A special case of a wave is an electromagnetic wave which can propagate through vacuum, e.g. radio, light, x rays. Waves transport energy and momentum and energy is required to generate waves The medium must have elastic properties 1/22/2018 Physics 214 Summer 2018 38
Wave properties There are two types of waves Longitudinal consists of the propagation of a series of compressions and rarefactions and the local movement of the medium is an oscillation back and forward along the direction of the wave Sound is one example Transverse where the movement of the medium is at right angles to the velocity of the wave. The strings of musical instruments is an example. anim0019.mov 1/22/2018 Physics 214 Summer 2018 39
Periodic waves One can propagate waves which are a single complicated pulse e.g. an explosion or a complicated continuous wave e.g. the wind. We will focus on regular repetitive waves λ These waves have a pattern which repeats and the length of one pattern is called the wavelength λ The number of patterns which pass a point/second is called the frequency f and if the time for one pattern to pass is T then f = 1/T v = λ/t = fλ 1/22/2018 Physics 214 Summer 2018 40
Waves on a string If we shake the end of a rope we can send a wave along the rope. The rope must be under tension in order for the wave to propagate v = (F/μ) F = TENSION μ = MASS/UNIT LENGTH 1/22/2018 Physics 214 Summer 2018 41
Standing waves If two identical waves exist on the same string but traveling in opposite directions the result can be standing waves in which some points never have a deflection. These are called nodes and some points oscillate between plus and minus the maximum amplitude, these are called antinodes. Standing waves provide the notes on musical instruments. When a string is secured at both ends and plucked or hit the generated waves will travel along the string and be reflected and set up standing waves. 1/22/2018 Physics 214 Summer 2018 42