Universe Video. Magnetic Materials and Magnetic Fields Lab Activity. Discussion of Magnetism and Magnetic Fields

Transcription

1 Date Zero Hour In Class Homework Magnetism Intro: Mechanical 1/5 Tue (A) Universe Video 1/6 Wed (B) 1/7 Thur (C) Magnetic Materials and Magnetic Fields Lab Activity 1/8 Fri (A) Discussion of Magnetism and Magnetic Fields Watch Magnetism video 1. Magnetic Fields of current carrying wires. Fill out WSQ google form 1/11 Mon (A) LSM Discuss magnetic fields of wires and the RHR Watch Magnetism video 2. Magnetic Force on moving charges. Fill out WSQ google form. 1/12 Tue (B) 1/13 Wed (C) 1/14 Thu (B) 1/15 Fri (C) Build a better Electromagnet Lab RHR forces, practice with directions In class notes on crossed E and B fields Mag Quiz 1. Field and Forces on Particles Magnetism Packet work Watch Magnetism video 3. Magnetic Force on current carrying wires. Fill out WSQ google form. 1/18 MON NO SCHOOL! MLK! 1/19 Tue (B) 1/20 Wed (C) 1/21 Thu (B) 1/22 Fri (C) Induction Lab Magnetism Quiz 2. Forces and Fields on a wire Magnetic forces on a wire Lab Activity Discussion of video 4 and induction Watch Magnetism video 4. Magnetic Induction. Fill out WSQ google form. 1/25 Mon (A) LSM & Club Pics 1/26 Tu (B) 1/27 We (C) Lenz s Law In class Notes with Demos and Discussion Induction Work 1/28 Th (B) 1/29 Fr (C) Build a Motor Lab Magnetism Quiz 3. Induction Finish Discussion on Induction and Packet Finish Packet 2/1 Mon (A) Review Topics in Magnetism and Induction Review for Test 2/2 Tue (B) 2/3 Wed (C) Magnetism and Induction Test 1

2 Unit Objectives (magnetism): The student is able to distinguish the characteristics that differ between monopole fields (gravitational field of spherical mass and electrical field due to single point charge) and dipole fields (electric dipole field and magnetic field) and make claims about the spatial behavior of the fields using qualitative or semiquantitative arguments based on vector addition of fields due to each point source, including identifying the locations and signs of sources from a vector diagram of the field. The student is able to apply mathematical routines to express the force exerted on a moving charged object by a magnetic field. (That magnetic force is perpendicular to the direction of velocity of the object and to the magnetic field and is proportional to the magnitude of q, v, and B. It also depends on the angle between the velocity, and the magnetic field vectors. Treatment is quantitative for angles of 0, 90, or 180 and qualitative for other angles.) The student is able to create a verbal or visual representation of a magnetic field around a long straight wire or a pair of parallel wires. (the direction of the field can be determined by a right-hand rule) The student is able to describe the orientation of a magnetic dipole placed in a magnetic field in general and the particular cases of a compass in the magnetic field of the Earth and iron filings surrounding a bar magnet. The student is able to use the representation of magnetic domains to qualitatively analyze the magnetic behavior of a bar magnet composed of ferromagnetic material. There is no beginning or end to the magnetic field it is a continuous loop. There is no magnetic north pole found isolated from a south pole. The student is able to use right-hand rules to analyze a situation involving a current-carrying conductor and a moving electrically charged object to determine the direction of the magnetic force exerted on the charged object due to the magnetic field created by the current-carrying conductor. The student is able to plan a data collection strategy appropriate to an investigation of the direction of the force on a moving electrically charged object caused by a current in a wire in the context of a specific set of equipment and instruments and analyze the resulting data to arrive at a conclusion. The student is able to use representations and models to qualitatively describe the magnetic properties of some materials that can be affected by magnetic properties of other objects in the system. (Ferromagnetic vs. Parmagentic and diamagnetism) Unit Objectives (Induction): Changing magnetic flux induces an emf in a system, with the magnitude of the induced emf equal to the rate of change in magnetic flux. When the magnetic field is constant, the induced emf is the magnetic field multiplied by the rate of change in area perpendicular to the magnetic field. The conservation of energy determines the direction ofthe induced emf relative to the change in the magnetic flux. The student is able to construct an explanation of the function of a simple electromagnetic device in which an induced emf is produced by a changing magnetic flux through an area defined by a current loop (i.e., a simple microphone or generator) or of the effect on behavior of a device in which an induced emf is produced by a constant magnetic field through a changing area. 2

3 Notes from in class Discussion of Magnetism and Magnetic Fields from permanent magnets: 3

4 Guided notes for video 1: Magnetic Fields from Current Carrying Wires What creates magnetism? Questions What is the symbol and unit for Magnetic Field? What effects the strength of a magnetic field from a current carrying wire? Words: Equation: What is the value of the constant of permeability of free space? What is the right hand rule and how do you use it to find the direction of a magnetic field of a current carrying wire? Draw the magnetic field direction for a wire with current traveling upwards as shown in the video. Draw the magnetic field for a loop carrying current counterclockwise. How are the directions into the page and out of the page symbolized? Practice problem, pause video and try this problem: A power line carries a current of 95 A along the tops of 8.5 m-high poles. What is the magnitude and direction of the magnetic field produced by this wire at the ground? 4

5 How do you determine the net magnetic field at a point in space when multiple wires are present? Practice problem, pause video and try this problem: Two parallel wires are separated by 6 cm. Wire 1 carries a current of 4 A & wire 2 carries a current of 6 A in the same direction. What is the resultant B-field at the midpoint between the wires? Where is the magnetic field of a solenoid the strongest and what factors affect it and what doesn t? What is the equation for calculating a magnetic field due to a solenoid? Summarize: on the google WSQ form for this video summarize what you learned. Make sure you discuss the source of magnetic fields, what factors affect them and how to determine their direction. Practice Questions: show work below and enter answer onto google form 1. What is the direction of the magnetic field due to a wire carrying current into the page: a. Clockwise b. Counterclockwise c. Into the page d. Out of the page 2. What is the direction of the net magnetic field midway between these two wires that are carrying equal magnitude current? a. Left b. Right c. Up d. Down e. zero 5

6 Guided notes for video 2: Magnetic Forces on Particles Moving in a Magnetic Field What were the contributions of Oersted and Ampere to magnetism? Questions Does a charged particle have to be moving to feel a magnetic force? What factors affect the magnitude of the force on the particle? Words: Equation: How does the angle of the motion of the particle to the magnetic field affect the force on the particle? Describe the right hand rule for forces on charged particles in magnetic fields. Practice problem, pause video and try this problem: A 2-nC charge is projected with velocity 5 x 10 4 m/s at an angle of 30 0 with a 3 mt magnetic field as shown. What are the magnitude and direction of the resulting force? Why do magnetic forces result in circular motion? Show how the equation for radius of the circular path is derived below: 6

7 What does the fact that the force is circular mean in terms of work done by magnetic forces? Practice problem, pause video and try this problem: Alpha particles of charge +1e and mass of 6.6 x kg are emitted from a radioactive source at a speed of 1.6 x 10 7 m/s. What magnetic field strength would be required to bend them into a circular path of radius of 0.25 m? Summarize: on the google WSQ form for this video summarize what you learned. Make sure you discuss the criteria for particles to experience a magnetic force and how you determine its direction. Practice Questions: show work below and enter answer onto google form 1. True or False? As long as a charged particle is moving in a magnetic field it will experience a magnetic force due to the field? 2. Determine the magnitude and direction of the force on an electron traveling horizontally to the east in a vertically upward magnetic field of strength 0.75 T at x 10 m/s In Class Notes on Crossed Electric and Magnetic Fields: 7

8 Guided notes for video 3: Magnetic Forces on Current Carrying Wires Using the right hand rule for forces on a current carrying wire, what does the direction of your: Thumb represent? Questions Fingers represent? Palm represent? How is the equation for a force on a current carrying wire derived from the force on a moving charge equation (F=qvB)? What is the equation for force on a current carrying wire at an angle to the magnetic field? Practice problem, pause video and try this problem: A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At that point on the Earth s surface, the dip angle of the Earth s magnetic field makes an angle of 38 to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth s magnetic field of at this point (B = 5.5x10-5 T). Why will a current carrying loop rotate in a magnetic field if the net force is zero? When is the magnetic force attractive current carrying between wires? When is the magnetic forces repulsive between current carrying wires? What is the equation for the mutual force per unit length of current carrying wires? Practice problem, pause video and try this problem: Two wires 5 cm apart carry currents. The upper wire has 4 A east and the lower wire has 6 A west. What is the mutual force per unit length on the wires? 8

9 Summarize: on the google WSQ form for this video summarize what you learned. Make sure you discuss what affect the magnetic force and how you use the RHR for wires. Practice Questions: show work below and enter answer onto google form 1. Determine the magnitude and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direction. 2. Is the force above attractive or repulsive? Guided notes for video 4: Magnetic Induction What did Faraday discover? Questions Describe the process for the generation of an electric field on a conductor moving in a magnetic field. Show the derivation of the equation for motional emf: Explain why a continuous force must be applied in order to keep a bar moving through the magnetic field? How do I calculate the magnitude of the force of pull to keep the bar moving at constant speed? 9

10 Practice problem, pause video and try this problem: The rod moves with a speed of 1.6 m/s is 30.0 cm long, and has a resistance of 2.5 W. The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is 25 W at a given instant. Calculate (a) the induced emf: b) the current in the U-shaped conductor (can you figure out its direction?) (c) the external force needed to keep the rod s velocity constant at that instant. What is magnetic flux and what factors affect it? What is the equation and unit for Magnetic Flux? List Faradays Observations for the generation of motional emf Write the Faraday s Law equation: Summarize: on the google WSQ form for this video summarize what you learned. Be sure to include information about what motional emf, what magnetic flux is and what factors affect it. Practice Questions: show work below and enter answer onto google form 1. A current loop has an area of 40 cm 2 and is placed in a 3-T B-field at the given angles. Find the flux F through the loop if the normal is parallel to the loop, perpendicular to the loop and at an angle of 60 degrees. You should have three answers, type them in order. 10

11 2. A 9.6-cm-diameter circular loop of wire is in a 1.10-T magnetic field. The loop is removed from the field in 0.15 s. What is the average induced emf? Notes for In Class Discussion of Lenz s Law: 11

12 In Class Work: Magnetism: 1. The compass needle shown below is free to rotate in the plane of the page. Either a bar magnet or a charged rod is brought toward the center of the compass. Does the compass rotate? If so does it rotate clockwise or counterclockwise? If not, why not? 4. Answer the questions below on the basis of your experience with charges and magnets. a. Based on your experience with electric field lines: i. how should the direction of the magnetic field at every point be related to the magnetic field lines? ii. how should the strength of the magnetic field at every point be reflected in the magnetic field lines 12

13 b. Carefully draw the magnetic field lines for the bar magnet shown below. Be sure to draw the field lines so that they include information about the strength and direction of the field both inside and outside the magnet. c. Based on the magnetic field lines you have drawn, rank the magnitude of the magnetic field at points A-E. 5. Two identical magnets are placed as shown. Using different colored pens sketch the approximate magnetic field vectors at the four labeled points for: just the horizontal top magnet, just the vertical bottom magnet, and when both are present. Explain how you determined the field vectors for the case when both magnets are present. 6. Three metal bars, labeled 1, 2, and 3, are marked A and B on either end as shown. The following observations are made by a student: end lb repels end 3A end la attracts end 2B end 2B attracts end 3B a. To which of your three classes from section I of the Lab Activity from the second day of the unit Magnets and magnetic fields could bar 1 belong? Explain your reasoning and the characteristics that define each of your classes. b. To which of your three classes could bar 2 belong? Explain your reasoning. c. Would end 2A attract, repel, or neither attract nor repel end 3A if the two ends were brought near one another? If it is not possible to tell for certain, what are the possibilities? Explain. 13

14 7. A neutral copper rod, a polarized insulator rod and a bar magnet are arranged around a current-carrying wire as shown. For each, will it stay where it is? Move toward or away from the wire? Rotate clockwise or counterclockwise? Explain. a. Neutral copper rod: b. Polarized insulator rod: c. Magnet: 8. For each of the current-carrying wires shown, draw a compass needle in its equilibrium orientation at the position of the dots. Label the poles of the compass needle. 9. The figure to the right shows a wire caring current perpendicular to the page. Draw the magnetic field lines around the wire. Draw the magnetic field vectors at a few points around the wire. 10. The following wires are carrying current in the plane of the page as shown. Draw the magnetic field above and below the wires. a. b. 11. Each figure below shown the two long straight wires carrying equal currents into and out of the page. At each of the dots, use a black pen or pencil to show and label the magnetic fields B1 and B2 of each wire. Then use a red pen or pencil to show the net magnetic field. a. b. 14

15 12. A long straight wire, perpendicular to the page, passes through a uniform magnetic field. The net magnetic field at point 3 is zero. a. On the figure, show the direction of the current in the wire. b. Points 1 and 2 are the same distance from the wire as point 3; point 4 is twice as distant. Construct vector diagrams at points 1, 2, and 4 to determine the net magnetic field at each point. 13. Rank in order, from largest to smallest, the magnetic field strength B1 to B3 produced by these three solenoids. 14. Suppose you need to find the magnetic field near the intersection of two long, straight, current- carrying wires. Assume that one wire lies directly on top of the other. Let the intersection of the wires be the origin of a coordinate system and let the point of interest, which is in the same plane, have coordinates (x, y). Recall that the magnetic field is a vector, having both a magnitude and a direction. a. What is the direction of magnetic field B 1 due to current I 1? b. Write an expression for the magnetic field produced by I 1. c. What is the direction of magnetic field B2 due to current I 2? d. Write an expression for the magnetic field produced by I 2. e. With knowing that I 1 > I 2, is it possible to determine the net direction of the magnetic field at point x,y? Why or why not? f. Let a magnetic field pointing out of the page have a positive value, one pointing into the page a negative value. This is actually Bz, the magnetic field along the z-axis. Use your results for parts a-d to write an expression for Bz at position (x, y). This will be a symbolic expression in terms of quantities defined on the figure. 15

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17 The magnetic field is constant magnitude inside the dotted lines and zero outside. Sketch and label the trajectory of the charge for a. A weak field. b. A strong field X X X X X X X X X X X X 4. A positive ion is shot between the plates of a parallel-plate capacitor. a. In what direction is the electric force on the ion? b. Could a magnetic field exert a magnetic force on the ion that is opposite in direction to the electric force? If so show the magnetic field on the figure. If not, why not? 5. A solenoid is wound as shown and attached to a battery. Two electrons are fired into the solenoid, one from the end and one through a very small hole in the side. a. In what direction does the magnetic field inside the solenoid point? Show it on the figure. b. Is electron I deflected as it moves through the solenoid? If so, in which direction? If not, why not? c. Is electron 2 deflected as it moves through the solenoid? If so, in which direction? If not, why not? 17

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19 Forces on Current Carrying Wires: 1. Three current-carrying wires are perpendicular to the page. Construct a force vector diagram on the figure to find the net force on the upper wire due to the two lower wires. 2. A current-carrying wire passes between two bar magnets. Is there a force on the wire? If so, draw the force vector. If not, why not? The current loop exerts a repulsive force on the bar magnet. On the figure, show the direction of the current in the loop. Explain. 5. The south pole of a bar magnet is held near a current loop. Does the bar magnet attract the loop, repel the loop, or have no effect on the loop? Explain. 6. A square current loop is placed in a magnetic field as shown. a. Does the loop undergo a displacement? If so, is it up, down, left, or right? If not, why not? b. Does the loop rotate? If so, which edge rotates out of the page and which edge into the page? If not, why not? 19

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21 B2007b2 A beam of particles of charge q = +3.2 x C and mass m = 6.68 x kg enters Region I with a range of velocities all in the direction shown in the diagram above. There is a magnetic field in Region I directed into the page with magnitude B = 0.12 T. Charged metal plates are placed in appropriate locations to create a uniform electric field of magnitude E = 4800 N/C in Region I. As a result, some of the charged particles pass straight through Region I undeflected. Gravitational effects are negligible. (a) i. On the diagram above, sketch electric field lines in Region I. ii. Calculate the speed of the particles that pass straight through Region I. The particles that pass straight through enter Region II in which there is no electric field and the magnetic field has the same magnitude and direction as in Region I. The path of the particles in Region II is a circular arc of radius R. (b) Calculate the radius R. (c) Within the beam there are particles moving slower than the speed you calculated in (a)ii. In what direction is the net initial force on these particles as they enter Region I? To the left Toward the top of the page Out of the plane of the page To the right Toward the bottom of the page Into the plane of the page Justify your answer. (d) A particle of the same mass and the same speed as in (a)ii but with charge q = 3.2 x C enters Region I. On the following diagram, sketch the complete resulting path of the particle. 21

22 295. The figure above shows a cross section of a cathode ray tube. An electron in the tube initially moves horizontally in the plane of the cross section at a speed of 2.0 x 10 7 meters per second. The electron is deflected upward by a magnetic field that has a field strength of 6.0 x 10-4 tesla. a. What is the direction of the magnetic field? b. Determine the magnitude of the magnetic force acting on the electron. c. Determine the radius of curvature of the path followed by the electron while it is in the magnetic field. An electric field is later established in the same region as the magnetic field such that the electron now passes through the magnetic and electric fields without deflection. d. Determine the magnitude of the electric field. e. What is the direction of the electric field? 22

23 889 The long, straight wire shown in Figure 1 above is in the plane of the page and carries a current I. Point P is also in the plane of the page and is a perpendicular distance d from the wire. Gravitational effects are negligible. a. With reference to the coordinate system in Figure 1, what is the direction of the magnetic field at point P due to the current in the wire? A particle of mass m and positive charge a is initially moving parallel to the wire with a speed do when it is at point P. as shown in Figure 2 below. b. With reference to the coordinate system in Figure 2, what is the direction of the magnetic force acting on the particle at point P? c. Determine the magnitude of the magnetic force acting on the particle at point P in terms of the given quantities and fundamental constants. d. An electric field is applied that causes the net force on the particle to be zero at point P. i. With reference to the coordinate system in Figure 2, what is the direction of the electric field at point P that could accomplish this? ii. Determine the magnitude of the electric field in terms of the given quantities and fundamental constants. 23

24 489. The magnitude of the magnetic field in teslas at a distance d from a long straight wire carrying a current I is given by the relation B = 2 X 10-7 I/d. The two long straight wires shown above are perpendicular, insulated from each other, and small enough so that they may be considered to be in the same plane. The wires are not free to move. Point P, in the same plane as the wires, is 0.5 meter from the wire carrying a current of 1 ampere and is 1.0 meter from the wire carrying a current of 3 amperes. a. What is the direction of the net magnetic field at P due to the currents? b. Determine the magnitude of the net magnetic field at P due to the currents. A charged particle at point P that is instantaneously moving with a velocity of 10 6 meters per second toward the top of the page experiences a force of 10-7 newtons to the left due to the two currents. c. State whether the charge on the particle is positive or negative. d. Determine the magnitude of the charge on the particle. e. Determine the magnitude and direction of an electric field also at point P that would make the net force on this moving charge equal to zero. 24

25 2011 form B 5. The diagram to the right illustrates a velocity selector, labeled region 1. It consists of two parallel conducting plates, with charges on the plates as indicated creating an electric field of magnitude E directed toward the top of the page. A uniform magnetic field of magnitude B 1 directed out of the page exists between the plates. The magnitude of the magnetic field can be adjusted so that only particles of a particular speed pass through the selector in a straight line. A radioactive source to the left of the selector emits charged particles, each having the same charge +q and moving to the right in the plane of the page. The effect of gravity can be neglected throughout the problem. a) i. Derive the equation v = E/ B 1 for the speed v of particles that move in a straight line through region 1. ii. Some particles are emitted from the source with speeds greater than E/ B 1. Which of the following describes the initial path of one of these particles immediately after entering region 1? Explain your reasoning. It curves toward the top of the page. It curves into the page. It moves in a straight line. It curves toward the bottom of the page. It curves out of the page. A constant magnetic field of magnitude B 2 directed into the page is now added in region 2 to the right of region 1, as represented in the figure to the right. Suppose a particle leaves the radioactive source, travels through region 1 in a straight line, and enters region 2. For each of the following, express algebraic answers in terms of E, B 1, B 2, q, and fundamental constants, as appropriate. (b) Determine an expression for the initial magnetic force on the particle in region 2 and state its direction. (c) Describe the changes, if any, in the magnitude and direction of the magnetic force as the particle moves in region 2. (d) Describe the path of the particle in region 2. (e) Derive an expression for the charge-to-mass ratio q/ m of the particle. Specifically note any quantities not previously defined that are included in your answer. 25

26 Induction Problems: 1. The figures below show one or more metal wires sliding on fixed metal rails in a magnetic field. For each, determine if the induced current flows clockwise, flows counterclockwise, or is zero. Show your answer by drawing it 2. A vertical, rectangular loop of copper wire is half in and half out of a horizontal magnetic field (shaded gray). The field is zero beneath the dashed line. The loop is released and starts to fall. a. Add arrows to the figure to show the direction of the induced current in the loop. b. Is there a net magnetic force on the loop? If so, in which direction? Explain 3. A metal bar rotates counterclockwise in a magnetic field as shown. Does the bar have a motional emf? If not, why not? If so, is the outer end of the bar positive or negative? Explain 4. The figure shows five loops in a magnetic field. The numbers indicate the lengths of the sides and the strength of the field. Rank in order, from largest to smallest, the magnetic fluxes. Some may be equal. 5. A circular loop rotates at constant speed about an axle through the center of the loop. The figure shows an edge view and defines the angle, which increases from 0 to 360 as the loop rotates. a. At what angle or angles is the magnetic flux a maximum? b. At what angle or angles is the magnetic flux a minimum? c. At what angle or angles is the magnetic flux changing most rapidly? Explain your choice. 26

27 6. A magnetic field is perpendicular to a loop. The graph shows how the magnetic field changes as a function of time, with positive values for B indicating a field into the page and negative values a field out of the page. Several points on the graph are labeled. a. At which lettered point or points is the flux through the loop a maximum? b. At which lettered point or points is the flux through the loop a minimum? c. At which point or points is the flux changing most rapidly? d. At which point or points is the flux changing least rapidly? 7. Does the loop of wire have a clockwise current, a counterclockwise current, or no current under the following circumstances? Explain. a. The magnetic field points out of the page and its strength is increasing. b. The magnetic field points out of the page and its strength is constant. c. The magnetic field points out of the page and its strength is decreasing. 8. A loop of wire is perpendicular to a magnetic field. The magnetic field strength as a function of time is given by the top graph. Draw a graph of the current in the loop as a function of time. Let a positive current represent a current that comes out of the top of the loop and enters the bottom of the loop. There are no numbers for the vertical axis, but your graph should have the correct shape and proportions. 27

28 Electromagnetic Induction Problems Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics! -- Wolfgang Pauli 28

29 Electromagnetic Induction Problems Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics! -- Wolfgang Pauli 29

30 Electromagnetic Induction Problems Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics! -- Wolfgang Pauli 2009 (3) A metal rod of mass 0.22 kg lies across two parallel conducting rails that are a distance of 0.52 m apart on a tabletop, as shown in the top view above. A 3.0 W resistor is connected across the left ends of the rails. The rod and rails have negligible resistance but significant friction with a coefficient of kinetic friction of There is a magnetic field of 0.80 T perpendicular to the plane of the tabletop. A string pulls the metal rod to the right with a constant speed of 1.8 m/s. (a) Calculate the magnitude of the current induced in the loop formed by the rod, the rails, and the resistor. (b) Calculate the magnitude of the force required to pull the rod to the right with constant speed. (c) Calculate the energy dissipated in the resistor in 2.0 s. (d) Calculate the work done by the string pulling the rod in 2.0 s. (e) Compare your answers to parts (c) and (d). Provide a physical explanation for why they are equal or unequal. 30

31 Electromagnetic Induction Problems Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics! -- Wolfgang Pauli A square loop of wire of side 0.20 m has a total resistance of 0.60 Ω. The loop is positioned in a uniform magnetic field B of T. The field is directed into the page, perpendicular to the plane of the loop, as shown above. (a) Calculate the magnetic flux through the loop. The field strength now increases uniformly to 0.20 T in 0.50 s. (b) Calculate the emf ε induced in the loop during this period. (c) i. Calculate the magnitude I of the current in the loop during this period. ii. What is the direction of the current in the loop? Clockwise Justify your answer. Counterclockwise (d) Describe a method by which you could induce a current in the loop if the magnetic field remained constant. 31

32 Electromagnetic Induction AP Problems 2003B3 A rail gun is a device that propels a projectile using a magnetic force. A simplified diagram of this device is shown above. The projectile in the picture is a bar of mass M and length D, which has a constant current I flowing through it in the +y-direction, as shown. The space between the thin frictionless rails contains a uniform magnetic field B, perpendicular to the plane of the page. The magnetic field and rails extend for a distance L. The magnetic field exerts a constant force F on the projectile, as shown. Express all algebraic answers to the following parts in terms of the magnitude F of the constant magnetic force, other quantities given above, and fundamental constants. a. Determine the position x of the projectile as a function of time t while it is on the rail if the projectile starts from rest at x = 0 when t = 0. b. Determine the speed of the projectile as it leaves the right-hand end of the track. c. Determine the energy supplied to the projectile by the rail gun. d. In what direction must the magnetic field B point in order to create the force F? Explain your reasoning. e. Calculate the speed of the bar when it reaches the end of the rail given the following values. B = 5 T L = 10 m I = 200 A M = 0.5 kg D = 10 cm 32

33 Electromagnetic Induction AP Problems 2010 #6. The plastic cart shown in the figure above has mass 2.5 kg and moves with negligible friction on a horizontal surface. Attached to the cart is a rigid rectangular loop of wire that is 0.10 m by 0.20 m, has resistance 4.0 W, and has a mass that is negligible compared to the mass of the cart. The plane of the rectangular loop is parallel to the plane of the page. A uniform magnetic field of 2.0 T, perpendicular to and directed into the plane of the page, starts at x = 0, as shown above. (a) On the figure below, indicate the direction of the induced current in the loop when its front edge is at x = 0.12 m. Justify your answer. (b) When the front edge of the rectangular loop is at for that instant at x = 0.12 m, its speed is 3.0 m/s. Calculate the following i. The magnitude of the induced current in the rectangular loop of wire ii. The magnitude of the net force on the loop (c) At a later time, the cart and loop are completely inside the magnetic field. Determine the magnitude of the net force on the loop at that time. Justify your answer. 33

34 Electromagnetic Induction AP Problems 528. A circular loop of wire of resistance 0.2 ohm encloses an area 0.3 square meter and lies flat on a wooden table as shown above. A magnetic field that varies with time t as shown below is perpendicular to the table. A positive value of B represents a field directed up from the surface of the table; a negative value represents a field directed into the tabletop. a. Calculate the value of the magnetic flux through the loop at time t = 3 seconds. b. Calculate the magnitude of the emf induced in the loop during the time interval t = 0 to 2 seconds. c. On the axes below, graph the current I through the coil as a function of time t, and put appropriate numbers on the vertical scale. Use the convention that positive values of I represent counterclockwise current as viewed from above. 34

35 Electromagnetic Induction AP Problems 468. A wire loop, 2 meters by 4 meters, of negligible resistance is in the plane of the page with its left end in a uniform 0.5-tesla magnetic field directed into the page, as shown above. A 5-ohm resistor is connected between points X and Y. The field is zero outside the region enclosed by the dashed lines. The loop is being pulled to the right with a constant velocity of 3 meters per second. Make all determinations for the time that the left end of the loop is still in the field, and points X and Y are not in the field. a. Determine the potential difference induced between points X and Y. b. On the figure above show the direction of the current induced in the resistor. c. Determine the force required to keep the loop moving at 3 meters per second. d. Determine the rate at which work must be done to keep the loop moving at 3 meters per second. 35

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