# Eðlisfræði 2, vor 2007

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 [ Assignment View ] [ Pri Eðlisfræði 2, vor a. Electromagnetic Induction Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline has passed. The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help. The unopened hint bonus is 2% per part. You are allowed 4 attempts per answer. Electromanetic Induction Conceptual Induction A loop of wire is initially held above a short solenoid. A constant counterclockwise (as viewed from above) current lowered, passing over the solenoid. passes through the coils of the solenoid. Suppose that the loop of wire is steadily When asked for the direction of current thoughout this problem, suppose that you are viewing the wire loop from above, looking downward. What is the direction of the induced current in the loop when the loop is above the solenoid, moving downward?.1 What is the direction of the magnetic field in the solenoid? To solve Parts A, B, and C, you will need to use Lenz's law. The current in the solenoid generates a magnetic field. As the wire loop approaches the solenoid, the magnetic flux passing through the loop (due to the solenoid's magnetic field) changes. A current will be induced in the loop, and the flux produced by this induced current must oppose the change in flux due to the solenoid's magnetic field. What is the direction of the magnetic field that passes through the interior of the solenoid? up down Hint A.2 Faraday's law You can think about this problem in terms of the Faraday's law. According to this law, the electromotive force (EMF) that produces current in the loop is given by, where is the magnetic flux through the loop. Pay attention at the minus sign. This minus sign means that if the magnetic flux is increasing, then the EMF is such that it produces the current whose induced magnetic field will be in the opposite direction to that of, while if the magnetic flux is decreasing, then the induced field is in the direction of. clockwise counterclockwise no current What is the direction of the induced current when the loop is at the midpoint of the solenoid and still moving downward? Hint B.1 Applying Lenz's law As the loop approaches the solenoid from above, the number of magnetic field lines passing through the loop due to the magnetic field of the solenoid increases. (The number of magnetic field lines passing through the loop represents the magnitude of the magnetic flux through the loop.) The number of field lines passing through the loop will continue to increase until the loop arrives at the midpoint of the solenoid. Once the loop travels beyond the solenoid's midpoint, the number of field lines passing through the loop begins to decrease. Therefore, when the loop is exactly at the midpoint of the solenoid, the number of field lines passing through the loop must be neither increasing nor decreasing. At the instant the wire loop is at the midpoint of the solenoid, there is no change in magnetic flux through the loop. clockwise counterclockwise no current What is the direction of the induced current when the loop is below the solenoid and moving downward? clockwise counterclockwise no current Page 1 of 7

2 Faraday's Law Introduction to Faraday's Law Learning Goal: To understand the terms in Faraday's law for magnetic induction of electric fields, and contrast these fields with those produced by static charges. Faraday's law describes how electric fields and electromotive forces are generated from changing magnetic fields. It relates the line integral of the electric field around a closed loop to the change in the total magnetic field integral across a surface bounded by that loop:, where is the line integral of the electric field, and the magnetic flux is given by, where is the angle between the magnetic field and the local normal to the surface bounded by the closed loop. Direction: The line integral and surface integral reverse their signs if the reference direction of or is reversed. The right-hand rule applies here: If the thumb of your right hand points along, then the fingers point along. You are free to take the loop anywhere you choose, although usually it makes sense to choose it to lie along the path of the circuit you are considering. Consider the direction of the electric field in the figure. Assume that the magnetic field points upward, as shown. Under what circumstances is the direction of the electric field shown in the figure correct? Hint A.1 There are two approaches: How to approach the problem One approach is to realize that the electric field would produce a current in the same direction as the field if there were a wire present. Find the magnetic field due to this (imaginary) current using the right-hand rule. The magnetic field produced by this current must oppose the change in the original magnetic field. You should be able to tell what the change is. The other approach is more mathematical. Choose a direction for and. Suppose is in the direction of the electric field shown. Then has the same direction as that of the magnetic field shown. The left-hand side of Faraday's equation is positive, and so is the magnetic flux. However, since the left-hand side is positive, the change in flux should be negative. What must have happened to the field? always if if increases with time decreases with time depending on whether your right thumb is pointing up or down Now consider the magnetic flux through a surface bounded by the loop. Which of the following statements about this surface must be true if you want to use Faraday's law to relate the magnetic flux to the line integral of the electric field around the loop? The surface must be the circular disk in the middle of the loop. The surface must be perpendicular to the magnetic field at each point. The surface can be any surface whose edge is the loop. The surface can be any surface whose edge is the loop as long as no magnetic field line passes through it more than once. You are free to take any surface bounded by the loop as the surface over which to evaluate the integral. The result will always be the same, owing to the continuity of magnetic field lines (they never start or end anywhere, since there are no magnetic charges). It is important to understand the vast differences between electric fields produced by changing magnetic fields via Faraday's law and the more familiar electric fields produced by charges via Coulomb's law. Here are some short questions that illustrate these differences. When can an electric field be measured at any point from the force on a stationary test charge at that point? Hint C.1 Force on a stationary charge Recall that the total force on a charge is. If the charge is stationary, i.e.,, then the force reduces to. only if the field is generated by the coulomb field of static charges Page 2 of 7

3 only if the field is generated by a changing magnetic field no matter how the field is generated In fact, this operation defines an electric field. Similarly, if the test charge is moving, it will measure magnetic fields. Part D When can an electric field that does not vary in time arise? only if the field is generated by a coulomb field of static charges only if the field is generated by a changing magnetic field in either of the above two cases Electric fields never vary in time; otherwise, a charge could gain energy from the field. Part E When will the integral around any closed loop of the projection of the electric field along that loop be zero? only if the field is generated by the coulomb field of static charges only if the field is generated by the coulomb field of static charges or a constant current only if the field is generated by a changing magnetic field however the field is generated The loop integral is always zero; otherwise, a charge moving around the loop would gain energy. The electric field generated by a static charge or a constant current always has zero loop integral. A constant current is a continuous line of evenly-spaced charges moving with constant velocity. An electric field generated by any other configuration of moving charges (moving through the loop) would have a non-zero loop integral. Here is a simple quantitative problem that uses Faraday's law. Part F A cylindrical iron rod of infinite length with cross-sectional area is oriented with its axis of symmetry coincident with the z axis of a cylindrical coordinate system as shown in the figure. It has a magnetic field inside that varies according to. Find the theta component of the electric field at distance from the z axis, where is larger than the radius of the rod. Hint F.1 Selecting the loop You want to find, but Faraday's law determines only an integral of the field. Therefore, you must pick the loop around which you will integrate in such a way that it involves only one value of and has a constant projection of along it. Such a loop is a circle with fixed (at any z, since the rod extends infinitely in the z direction). Part F.2 Find the magnetic flux Faraday's law states that. Therefore, to find the electric field you must first find the magnetic flux. What is the magnetic flux at time? Hint F.2.a The flux integral The flux integral for a constant field is the product of the magnitude of the perpendicular magnetic field and the area over which the integral is evaluated. Express your answer in terms of the magnetic field variables and,, and. = Part F.3 Finding the EMF from Faraday's law From the previous part, you found that. According to Faraday's law,. Use your equation for to find the EMF predicted by Faraday's law. Express your answer in terms of,,,, and any necessary constants. = Hint F.4 Help from symmetry The rod extends along the entire z axis, so the electric field cannot depend on. Since the rod is cylindrically symmetric, the field cannot depend on either. Thus, the component of the electric field is a function only of. Page 3 of 7

4 Part F.5 Find the EMF in terms of By definition, the EMF around a loop is given by. The dot product means that you need consider only the component of parallel to. Find the relationship between and. Hint F.5.a The component of the field along the loop Since the loop is a circle with constant but varying, the component of the electric field is the component along the loop. Express in terms of, quantities given in the introduction to this part, and familiar constants. = Answer not displayed Express your answer in terms of,,,, and any needed constants such as,, and. = Electric Field Due to Increasing Flux Learning Goal: To work through a straightforward application of Faraday's law to find the EMF and the electric field surrounding a region of increasing flux Faraday's law describes how electric fields and electromotive forces are generated from changing magnetic fields. This problem is a prototypical example in which an increasing magnetic flux generates a finite line integral of the electric field around a closed loop that surrounds the changing magnetic flux through a surface bounded by that loop. A cylindrical iron rod with cross-sectional area is oriented with its symmetry axis coincident with the z axis of a cylindrical coordinate system as shown. It has a uniform magnetic field inside that varies according to the magentic field is always in the positive z direction, and it has no other components. For your convenience, we restate Faraday's law here:, where is the line integral of. In other words, the electric field, and the magnetic flux is given by, where is the angle between the magnetic field and the local normal to the surface bounded by the closed loop. Direction: The line integral and surface integral reverse their signs if the reference direction of or is reversed. The right-hand rule applies here: If the thumb of your right hand is taken along, then the fingers point along. You are free to take the loop anywhere you choose, although usually it makes sense to choose it to lie along the path of the circuit you are considering. Find, the electromotive force (EMF) around a loop that is at distance from the z axis, where is restricted to the region outside the iron rod as shown. Take the direction shown in the figure as positive. Hint A.1.2 Selecting the loop Find the magnetic flux Hint not displayed Express in terms of,,,, and any needed constants such as,, and. = Answer not displayed Due to the cylindrical symmetry of this problem, the induced electric field can depend only on the distance from the z axis, where is restricted to the region outside the iron rod. Find this field..1 Hint B.2 Calculate the line integral The z and r components of the electric field Hint not displayed Express in terms of quantities given in the introduction (and constants), using the unit vectors in the cylindrical coordinate system,,, and. = Answer not displayed Motion-Induced EMF's Motion-Induced Electric Fields and Motional EMF Page 4 of 7

5 Learning Goal: To understand that the motion of a conductor through a magnetic field generates a perpendicular electric field. A conducting rod of length is moved at a constant velocity through a uniform magnetic field. This field runs perpendicularly out of the page. The end of the rod at is labeled a, and the end of the rod at is labeled b. As a result of the motion through the magnetic field, a charge in the rod will experience a force : the usual part of the Lorentz force for charges moving through magnetic fields. This force will push the charge in the rod, and hence this force will be an electromotive force (EMF). For now, we shall say that the force that moves the charges is due to an induced electric field, which will enable us to calculate the EMF. The fact that there is an induced electric field at all is rather subtle, because there is no closed loop that encloses some changing flux. Therefore, a method that does not involve Faraday's law must be used to solve this motional EMF problem. In fact, this problem is a good introduction to some of the ideas behind Faraday's law. Find the y component of the induced electric field..1.2 Find the force on a charge due to motion in the magnetic field Find an equivalent electric field Express your answer in terms of the variables given in the problem introduction. = Answer not displayed There is a big complication in measuring the EMF generated by the moving rod: The wires that connect the meter to the rod also move through the magnetic field, and therefore, there is an electromotive force for them also. This is a general problem: A voltmeter can measure the EMF produced only in a closed loop around the circuit. In general, the EMF caused by the motion of a rod through a uniform magnetic field will be canceled by the opposite EMF induced by the motion of the rest of the circuit through this same uniform field. The only way to get a nonzero voltmeter reading is to make the field nonuniform, for example, such that the bar is moving through a region of nonzero field, but the rest of the circuit is (temporarily) moving in a region of zero field. For example, consider the arrangement shown in the figure for measuring the EMF in the moving rod using a voltmeter. In this arrangement, only for and. The hookup wires and voltmeter will have to move with the rod; they are rigid and of the dimensions and shape shown. The physical setup is that shown at the end of. Which graph shown best represents the magnitude of that will be measured by the voltmeter? Take to be the moment pictured in the diagram. Hint C.1.2 How to approach the problem Describe the EMF when only the rod moves through the field Hint not displayed.3 Describe the EMF when the whole circuit is moving through the field Answer not displayed Part D Page 5 of 7

6 Rail Gun This problem explores how a current-carrying wire can be accelerated by a magnetic field. You will use the ideas of magnetic flux and the EMF due to change of flux through a loop. Note that there is an involved follow-up part that will be shown once you have found the answer to. A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength in series with a resistor of resistance makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure. There is a uniform magnetic field of magnitude, pervading all space, perpendicular to the plane of rod and rails. The rod is released from rest, and it is observed that it accelerates to the left. In what direction does the magnetic field point? Hint A.1 The force on a conducting rod due to a magnetic field There is a force on the rod because a current is flowing through it. Hence charges are moving perpendicular to the magnetic field. The rod experiences a force, which is given by. Hint A.2 The direction of the magnetic field Use the right-hand rule with the cross product: Take your right hand and point with your index finger in the direction of the rail's motion, and point your middle finger in the direction of. Your thumb will then point in the direction of the magnetic field. into the plane of the figure out of the plane of the figure Assuming that the rails have no resistance, what is the most accurate qualitative description of the motion of the rod? Hint B.1 Lenz's law An EMF is induced in the circuit due to the change in magnetic flux through it. But will this EMF increase the current through the loop or decrease it by opposing the voltage coming from the source? Lenz's law states that induced currents will always flow in such a way that they oppose the change in flux that caused them. Hint B.2 Appyling Lenz's law to this problem Let us apply Lenz's law here. We want to find the direction of the induced current. The change in flux that induced this current is caused by the motion of the rod, which in turn is caused by the current flowing around the circuit due to the voltage source. The induced current works against that source current, and reduces it. Alternatively, one could say that the induced EMF opposes the voltage from the source. Hint B.3 The velocity of the rod The higher the velocity of the rod, the higher the induced EMF, and the lower the current flowing through the loop. But the force accelerating the rod is proportional to the current. Hence the acceleration goes down as the velocity goes up. The velocity cannot increase beyond the point at which the induced EMF is equal and opposite to. The rod will accelerate but the magnitude of the acceleration will decrease with time; the velocity of the rod will approach but never exceed a certain terminal velocity. Under these idealized conditions the rod will experience constant acceleration and the velocity of the rod will increase indefinitely. The rod will accelerate indefinitely with acceleration proportional to its (increasing) velocity. What is the acceleration of the rod? Take to be the mass of the rod..1 Find the induced EMF To determine the current, we need the EMF induced by the change in magnetic flux through the current loop of area. Faraday's law states that. The motion of the rod will change according to. What is the EMF? Express in terms of the velocity, the separation of the rails, and the magnetic field. =.2 Find the current in the rod We can find the current through the rail by using Kirchhoff's rule for a closed circuit:, where is the induced EMF. What is the current? Express your answer in terms of and other given quantities. Page 6 of 7

7 =.3 Find the acceleration of the rod To find the acceleration, we need the force on the rod. We have already determined its direction. The magnitude of this force is given in.i. Write down an expression for, using Newton's second law. Expres your answer in terms of mass, current,, and. = Express your answer as a function of,, the velocity of the rod,,, and the mass of the rod. = Making the substitution, you obtain the dfferential equation, which you can solve to find the velocity of the rod as a function of time:. To achieve a high acceleration, which is necessary for a useful gun, a magnetic field of large magnitude and a high voltage are advantageous. Part D What is the terminal velocity reached by the rod? Part D.1 Find an expression for the terminal velocity = A larger magnetic field increases the acceleration of the rod, but lowers the terminal velocity: a trade-off for rail gun engineers! Summary 3 of 5 problems complete (44.22% avg. score) 9.55 of 12 points Page 7 of 7

### Force on Moving Charges in a Magnetic Field

[ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

### 1 of 7 4/13/2010 8:05 PM

Chapter 33 Homework Due: 8:00am on Wednesday, April 7, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy [Return to Standard Assignment View] Canceling a Magnetic Field

### Eðlisfræði 2, vor 2007

[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline

### Objectives for the standardized exam

III. ELECTRICITY AND MAGNETISM A. Electrostatics 1. Charge and Coulomb s Law a) Students should understand the concept of electric charge, so they can: (1) Describe the types of charge and the attraction

### Eðlisfræði 2, vor 2007

[ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has

### Gauss's Law. Gauss's Law in 3, 2, and 1 Dimension

[ Assignment View ] [ Eðlisfræði 2, vor 2007 22. Gauss' Law Assignment is due at 2:00am on Wednesday, January 31, 2007 Credit for problems submitted late will decrease to 0% after the deadline has passed.

### The purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.

260 17-1 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this

### Electromagnetic Induction

. Electromagnetic Induction Concepts and Principles Creating Electrical Energy When electric charges move, their electric fields vary. In the previous two chapters we considered moving electric charges

### Chapter 20. Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields

Chapter 20 Magnetic Induction Changing Magnetic Fields yield Changing Electric Fields Introduction The motion of a magnet can induce current in practical ways. If a credit card has a magnet strip on its

### Physics 126 Practice Exam #3 Professor Siegel

Physics 126 Practice Exam #3 Professor Siegel Name: Lab Day: 1. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? A) The magnetic force

### Physics 1653 Exam 3 - Review Questions

Physics 1653 Exam 3 - Review Questions 3.0 Two uncharged conducting spheres, A and B, are suspended from insulating threads so that they touch each other. While a negatively charged rod is held near, but

### ElectroMagnetic Induction. AP Physics B

ElectroMagnetic Induction AP Physics B What is E/M Induction? Electromagnetic Induction is the process of using magnetic fields to produce voltage, and in a complete circuit, a current. Michael Faraday

### Name: Lab Partner: Section: The purpose of this lab is to study induction. Faraday s law of induction and Lenz s law will be explored.

Chapter 8 Induction - Faraday s Law Name: Lab Partner: Section: 8.1 Purpose The purpose of this lab is to study induction. Faraday s law of induction and Lenz s law will be explored. 8.2 Introduction It

### Kirchhoff's Rules and Applying Them

[ Assignment View ] [ Eðlisfræði 2, vor 2007 26. DC Circuits Assignment is due at 2:00am on Wednesday, February 21, 2007 Credit for problems submitted late will decrease to 0% after the deadline has passed.

### Electricity and Water Analogy

[ Assignment View ] [ Eðlisfræði 2, vor 2007 25. Current, Resistance, and Electromagnetic Force Assignment is due at 2:00am on Wednesday, February 14, 2007 Credit for problems submitted late will decrease

### Electromagnetic Induction. Physics 231 Lecture 9-1

Electromagnetic Induction Physics 231 Lecture 9-1 Induced Current Past experiments with magnetism have shown the following When a magnet is moved towards or away from a circuit, there is an induced current

### Chapter 14: Magnets and Electromagnetism

Chapter 14: Magnets and Electromagnetism 1. Electrons flow around a circular wire loop in a horizontal plane, in a direction that is clockwise when viewed from above. This causes a magnetic field. Inside

### AP Physics C Chapter 23 Notes Yockers Faraday s Law, Inductance, and Maxwell s Equations

AP Physics C Chapter 3 Notes Yockers Faraday s aw, Inductance, and Maxwell s Equations Faraday s aw of Induction - induced current a metal wire moved in a uniform magnetic field - the charges (electrons)

### (b) Draw the direction of for the (b) Draw the the direction of for the

2. An electric dipole consists of 2A. A magnetic dipole consists of a positive charge +Q at one end of a bar magnet with a north pole at one an insulating rod of length d and a end and a south pole at

### 1. The diagram below represents magnetic lines of force within a region of space.

1. The diagram below represents magnetic lines of force within a region of space. 4. In which diagram below is the magnetic flux density at point P greatest? (1) (3) (2) (4) The magnetic field is strongest

### SCS 139 II.3 Induction and Inductance

SCS 139 II.3 Induction and Inductance Dr. Prapun Suksompong prapun@siit.tu.ac.th L d dt di L dt B 1 Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20 Review + New Fact Review Force

### Ch.20 Induced voltages and Inductance Faraday s Law

Ch.20 Induced voltages and Inductance Faraday s Law Last chapter we saw that a current produces a magnetic field. In 1831 experiments by Michael Faraday and Joseph Henry showed that a changing magnetic

### Induction. d. is biggest when the motor turns fastest.

Induction 1. A uniform 4.5-T magnetic field passes perpendicularly through the plane of a wire loop 0.10 m 2 in area. What flux passes through the loop? a. 5.0 T m 2 c. 0.25 T m 2 b. 0.45 T m 2 d. 0.135

### Chapter 14 Magnets and

Chapter 14 Magnets and Electromagnetism How do magnets work? What is the Earth s magnetic field? Is the magnetic force similar to the electrostatic force? Magnets and the Magnetic Force! We are generally

### Eðlisfræði 2, vor 2007

[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 31. Alternating Current Circuits Assignment is due at 2:00am on Wednesday, March 21, 2007 Credit for problems submitted late will decrease to 0% after the

### Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.

### physics 112N electromagnetic induction

physics 112N electromagnetic induction experimental basis of induction! seems we can induce a current in a loop with a changing magnetic field physics 112N 2 magnetic flux! useful to define a quantity

### Solution Derivations for Capa #10

Solution Derivations for Capa #10 1) A 1000-turn loop (radius = 0.038 m) of wire is connected to a (25 Ω) resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the

### Tuesday, 9 August 2016

Tuesday, 9 August 2016 Conceptual Problem 34.10 a When the switch on the left is closed, which direction does current flow in the meter on the right: 1. Right to left 2. Left to right 3. There is no induced

### Physics 2212 GH Quiz #4 Solutions Spring 2015

Physics 1 GH Quiz #4 Solutions Spring 15 Fundamental Charge e = 1.6 1 19 C Mass of an Electron m e = 9.19 1 31 kg Coulomb constant K = 8.988 1 9 N m /C Vacuum Permittivity ϵ = 8.854 1 1 C /N m Earth s

### Faraday s Law Challenge Problem Solutions

Faraday s Law Challenge Problem Solutions Problem 1: A coil of wire is above a magnet whose north pole is pointing up. For current, counterclockwise when viewed from above is positive. For flux, upwards

### PHYS 155: Final Tutorial

Final Tutorial Saskatoon Engineering Students Society eric.peach@usask.ca April 13, 2015 Overview 1 2 3 4 5 6 7 Tutorial Slides These slides have been posted: sess.usask.ca homepage.usask.ca/esp991/ Section

### Physics 12 Study Guide: Electromagnetism Magnetic Forces & Induction. Text References. 5 th Ed. Giancolli Pg

Objectives: Text References 5 th Ed. Giancolli Pg. 588-96 ELECTROMAGNETISM MAGNETIC FORCE AND FIELDS state the rules of magnetic interaction determine the direction of magnetic field lines use the right

### Q28.1 A positive point charge is moving to the right. The magnetic field that the point charge produces at point P (see diagram below) P

Q28.1 A positive point charge is moving to the right. The magnetic field that the point charge produces at point P (see diagram below) P r + v r A. points in the same direction as v. B. points from point

### Chapter 29 Electromagnetic Induction

Chapter 29 Electromagnetic Induction - Induction Experiments - Faraday s Law - Lenz s Law - Motional Electromotive Force - Induced Electric Fields - Eddy Currents - Displacement Current and Maxwell s Equations

### Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region

### PHY2049 Exam #2 Solutions Fall 2012

PHY2049 Exam #2 Solutions Fall 2012 1. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial segments. The circuits

### Linear DC Motors. 15.1 Magnetic Flux. 15.1.1 Permanent Bar Magnets

Linear DC Motors The purpose of this supplement is to present the basic material needed to understand the operation of simple DC motors. This is intended to be used as the reference material for the linear

### MASSACHUSETTS INSTINUTE OF TECHNOLOGY ESG Physics. Problem Set 9 Solution

MASSACHUSETTS INSTINUTE OF TECHNOLOGY ESG Physics 8. with Kai Spring 3 Problem 1: 3-7 and 8 Problem Set 9 Solution A conductor consists of a circular loop of radius R =.1 m and two straight, long sections,

### Physics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5

Solutions to Homework Questions 5 Chapt19, Problem-2: (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat

### Chapter 23 Magnetic Flux and Faraday s Law of Induction

Chapter 23 Magnetic Flux and Faraday s Law of Induction 23.1 Induced EMF 23.2 Magnetic Flux 23.3 Faraday s Law of Induction 23.4 Lenz s Law 23.5 Mechanical Work and Electrical Energy 23.6 Generators and

### Conceptual: 1, 3, 5, 6, 8, 16, 18, 19. Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65. Conceptual Questions

Conceptual: 1, 3, 5, 6, 8, 16, 18, 19 Problems: 4, 6, 8, 11, 16, 20, 23, 27, 34, 41, 45, 56, 60, 65 Conceptual Questions 1. The magnetic field cannot be described as the magnetic force per unit charge

### Chapter 31. Faraday s Law

Chapter 31 Faraday s Law Michael Faraday 1791 1867 British physicist and chemist Great experimental scientist Contributions to early electricity include: Invention of motor, generator, and transformer

### Chapter 14 Magnets and Electromagnetism

Chapter 14 Magnets and Electromagnetism Magnets and Electromagnetism In the 19 th century experiments were done that showed that magnetic and electric effects were just different aspect of one fundamental

### 1 of 7 10/1/2012 3:17 PM

Assignment Previewer http://www.webassign.net/v4cgijfederici@njit/control.pl 1 of 7 10/1/2012 3:17 PM HW11Faraday (2861550) Question 1 2 3 4 5 6 7 8 9 10 1. Question Details SerPSE8 31.P.011.WI. [1742725]

### Review Questions PHYS 2426 Exam 2

Review Questions PHYS 2426 Exam 2 1. If 4.7 x 10 16 electrons pass a particular point in a wire every second, what is the current in the wire? A) 4.7 ma B) 7.5 A C) 2.9 A D) 7.5 ma E) 0.29 A Ans: D 2.

### ELECTROMAGNETISM I. CAUSES OF MAGNETISM

I. CAUSES OF MAGNETISM ELECTROMAGNETISM 1. Moving electric fields (moving charges) cause magnetism. Yes, that current moving in electric circuits cause a magnetic field. More later! 2. Elementary nature

### Chapter 30 - Magnetic Fields and Torque. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 30 - Magnetic Fields and Torque A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should

### physics 112N current, resistance and dc circuits

physics 112N current, resistance and dc circuits current! previously we considered electrostatic situations in which no E-field could exist inside a conductor! now we move to the case where an electric

### Physics 2220 Module 09 Homework

Physics 2220 Module 09 Homework 01. A potential difference of 0.050 V is developed across the 10-cm-long wire of the figure as it moves though a magnetic field perpendicular to the page. What are the strength

### MOVING CHARGES AND MAGNETISM

MOVING CHARGES AND MAGNETISM 1. A circular Coil of 50 turns and radius 0.2m carries of current of 12A Find (a). magnetic field at the centre of the coil and (b) magnetic moment associated with it. 3 scores

### 5K10.20 Induction Coil with Magnet, Galvanometer

5K10.20 Induction Coil with Magnet, Galvanometer Abstract When a magnet is moved through a coil of wire, a current is induced in the coil. A galvanometer connected to the coil measures this induced current.

### Magnetic Forces and Magnetic Fields

1 Magnets Magnets are metallic objects, mostly made out of iron, which attract other iron containing objects (nails) etc. Magnets orient themselves in roughly a north - south direction if they are allowed

### Faraday's Law da B B r r Φ B B A d dφ ε B = dt

Faraday's Law da Φ ε = r da r dφ dt Applications of Magnetic Induction AC Generator Water turns wheel rotates magnet changes flux induces emf drives current Dynamic Microphones (E.g., some telephones)

### Faraday s Law of Induction

Chapter 10 Faraday s Law of Induction 10.1 Faraday s Law of Induction...10-10.1.1 Magnetic Flux...10-3 10.1. Lenz s Law...10-5 10. Motional EMF...10-7 10.3 Induced Electric Field...10-10 10.4 Generators...10-1

### Physics 6C, Summer 2006 Homework 1 Solutions F 4

Physics 6C, Summer 006 Homework 1 Solutions All problems are from the nd edition of Walker. Numerical values are different for each student. Chapter Conceptual Questions 18. Consider the four wires shown

### Physics 9 Fall 2009 Homework 8 - Solutions

1. Chapter 34 - Exercise 9. Physics 9 Fall 2009 Homework 8 - s The current in the solenoid in the figure is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop?

### ) 0.7 =1.58 10 2 N m.

Exam 2 Solutions Prof. Paul Avery Prof. Andrey Korytov Oct. 29, 2014 1. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides, each with length L = 15 cm as

### Chapter 27 Magnetic Induction. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

Chapter 27 Magnetic Induction Motional EMF Consider a conductor in a B-field moving to the right. In which direction will an electron in the bar experience a magnetic force? V e - V The electrons in the

### Your Comments. I got so confused with Faraday's Law and Lenz's Law... AREN'T THESE TWO LAWS SUPPOSED TO MEAN THE SAME THING???

Your Comments There were some parts of this prelecture I grasped well while other parts like the generator and the loops I still have trouble with. Can you please clarify how Faraday's and Lenz's law are

### Induced voltages and Inductance Faraday s Law

Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic

### Physics Notes for Class 12 Chapter 4 Moving Charges and Magnetrism

1 P a g e Physics Notes for Class 12 Chapter 4 Moving Charges and Magnetrism Oersted s Experiment A magnetic field is produced in the surrounding of any current carrying conductor. The direction of this

### PSS 27.2 The Electric Field of a Continuous Distribution of Charge

Chapter 27 Solutions PSS 27.2 The Electric Field of a Continuous Distribution of Charge Description: Knight Problem-Solving Strategy 27.2 The Electric Field of a Continuous Distribution of Charge is illustrated.

### Module 3 : Electromagnetism Lecture 13 : Magnetic Field

Module 3 : Electromagnetism Lecture 13 : Magnetic Field Objectives In this lecture you will learn the following Electric current is the source of magnetic field. When a charged particle is placed in an

### Chap 21. Electromagnetic Induction

Chap 21. Electromagnetic Induction Sec. 1 - Magnetic field Magnetic fields are produced by electric currents: They can be macroscopic currents in wires. They can be microscopic currents ex: with electrons

### 2. B The magnetic properties of a material depend on its. A) shape B) atomic structure C) position D) magnetic poles

ame: Magnetic Properties 1. B What happens if you break a magnet in half? A) One half will have a north pole only and one half will have a south pole only. B) Each half will be a new magnet, with both

### Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 12 Solutions

Concept Check (top) Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 1 Solutions Student Book page 583 Concept Check (bottom) The north-seeking needle of a compass is attracted to what is called

### BASANT S SCIENCE ACADEMY STUDY MATERIAL MAGNETIC EFFECT OF CURRENT

BASANT S SCIENCE ACADEMY Why does a compass needle get deflected when brought near a bar magnet? A compass needle is a small bar magnet. When it is brought near a bar magnet, its magnetic field lines interact

### Magnetic Field of a Circular Coil Lab 12

HB 11-26-07 Magnetic Field of a Circular Coil Lab 12 1 Magnetic Field of a Circular Coil Lab 12 Equipment- coil apparatus, BK Precision 2120B oscilloscope, Fluke multimeter, Wavetek FG3C function generator,

### Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

### Faraday s Law and Inductance

Historical Overview Faraday s Law and Inductance So far studied electric fields due to stationary charges and magentic fields due to moving charges. Now study electric field due to a changing magnetic

### Electromagnetic Induction

Electromagnetic Induction PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html previously: electric currents generate magnetic field. If a current

### ! = "d# B. ! = "d. Chapter 31: Faraday s Law! One example of Faraday s Law of Induction. Faraday s Law of Induction. Example. ! " E da = q in.

Chapter 31: Faraday s Law So far, we e looked at: Electric Fields for stationary charges E = k dq " E da = q in r 2 Magnetic fields of moing charges d = µ o I # o One example of Faraday s Law of Induction

### PHYSICS 212 INDUCED VOLTAGES AND INDUCTANCE WORKBOOK ANSWERS

PHYSICS 212 CHAPTER 20 INDUCED VOLTAGES AND INDUCTANCE WORKOOK ANSWERS STUDENT S FULL NAME (y placing your name above and submitting this for credit you are affirming this to be predominantly your own

### 6. ELECTROMAGNETIC INDUCTION

6. ELECTROMAGNETIC INDUCTION Questions with answers 1. Name the phenomena in which a current induced in coil due to change in magnetic flux linked with it. Answer: Electromagnetic Induction 2. Define electromagnetic

### RUPHYS ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman

Signed in as Jolie Cizewski, Instructor Help Sign Out RUPHYS2272014 ( MPCIZEWSKI15079 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman Course Home Assignments Roster

### Chapter 5. Magnetostatics and Electromagnetic Induction

Chapter 5. Magnetostatics and Electromagnetic Induction 5.1 Magnetic Field of Steady Currents The Lorentz force law The magnetic force in a charge q, moving with velocity v in a magnetic field B in a magnetic

This test covers Faraday s Law of induction, motional emf, Lenz s law, induced emf and electric fields, eddy currents, self-inductance, inductance, RL circuits, and energy in a magnetic field, with some

### Magnetostatics II. Lecture 24: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay

Magnetostatics II Lecture 4: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Magnetic field due to a solenoid and a toroid A solenoid is essentially a long current loop

Copyright 2014 Edmentum - All rights reserved. Science Physics Electromagnetic Blizzard Bag 2014-2015 1. Two coils of insulated wire are placed side by side, as shown in the illustration. The blue lines

### 4/16/ Bertrand

Physics B AP Review: Electricity and Magnetism Name: Charge (Q or q, unit: Coulomb) Comes in + and The proton has a charge of e. The electron has a charge of e. e = 1.602 10-19 Coulombs. Charge distribution

### Magnetic Fields; Sources of Magnetic Field

This test covers magnetic fields, magnetic forces on charged particles and current-carrying wires, the Hall effect, the Biot-Savart Law, Ampère s Law, and the magnetic fields of current-carrying loops

### Home Work 9. i 2 a 2. a 2 4 a 2 2

Home Work 9 9-1 A square loop of wire of edge length a carries current i. Show that, at the center of the loop, the of the magnetic field produced by the current is 0i B a The center of a square is a distance

### Outline. Tom Browder (University of Hawaii) Faraday s Law and Magnetic Induction. AC electric generator is based on Faraday s Law

Outline Tom Browder (University of Hawaii) Faraday s Law and Magnetic Induction AC electric generator is based on Faraday s Law Headline Solar flare: Biggest in six years hits the Earth Solar flare: The

### Multiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields

Multiple Choice Questions for Physics 1 BA113 Chapter 23 Electric Fields 63 When a positive charge q is placed in the field created by two other charges Q 1 and Q 2, each a distance r away from q, the

### AP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path.

A charged particle is projected from point P with velocity v at a right angle to a uniform magnetic field directed out of the plane of the page as shown. The particle moves along a circle of radius R.

### 2. In Newton s universal law of gravitation the masses are assumed to be. B. masses of planets. D. spherical masses.

Practice Test: 41 marks (55 minutes) Additional Problem: 19 marks (7 minutes) 1. A spherical planet of uniform density has three times the mass of the Earth and twice the average radius. The magnitude

### My lecture slides are posted at Information for Physics 112 midterm, Wednesday, May 2

My lecture slides are posted at http://www.physics.ohio-state.edu/~humanic/ Information for Physics 112 midterm, Wednesday, May 2 1) Format: 10 multiple choice questions (each worth 5 points) and two show-work

### Module 3 : MAGNETIC FIELD Lecture 15 : Biot- Savarts' Law

Module 3 : MAGNETIC FIELD Lecture 15 : Biot- Savarts' Law Objectives In this lecture you will learn the following Study Biot-Savart's law Calculate magnetic field of induction due to some simple current

### Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:

Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.

### Phys 102 Spg Exam No. 2 Solutions

Phys 102 Spg. 2008 Exam No. 2 Solutions I. (20 pts) A 10-turn wire loop measuring 8.0 cm by 16.0 cm carrying a current of 2.0 A lies in the horizontal plane and is free to rotate about a horizontal axis

### 2015 Pearson Education, Inc. Section 24.5 Magnetic Fields Exert Forces on Moving Charges

Section 24.5 Magnetic Fields Exert Forces on Moving Charges Magnetic Fields Sources of Magnetic Fields You already know that a moving charge is the creator of a magnetic field. Effects of Magnetic Fields

### VII MAXWELL S EQUATIONS

VII MAXWELL S EQUATIONS 71 The story so far In this section we will summarise the understanding of electromagnetism which we have arrived at so far We know that there are two fields which must be considered,

### Lesson 11 Faraday s Law of Induction

Lesson 11 Faraday s Law of Induction Lawrence B. Rees 006. You may make a single copy of this document for personal use without written permission. 11.0 Introduction In the last lesson, we introduced Faraday

### Dr. Todd Satogata (ODU/Jefferson Lab) Monday, March

Vector pointing OUT of page Vector pointing N to page University Physics 227N/232N Review: Gauss s Law and Ampere s Law Solenoids and Magnetic nductors Lab rescheduled for Wednesday, March 26 in Scale-Up

### Lab 7: Faraday Effect and Lenz law Physics 208. What should I be thinking about before I start this lab?

Lab 7: Faraday Effect and Lenz law Physics 208 Name Section This sheet is the lab document your TA will use to score your lab. It is to be turned in at the end of lab. To receive full credit you must use

### Chapter 19 Magnetism Magnets Poles of a magnet are the ends where objects are most strongly attracted Two poles, called north and south Like poles

Chapter 19 Magnetism Magnets Poles of a magnet are the ends where objects are most strongly attracted Two poles, called north and south Like poles repel each other and unlike poles attract each other Similar

### * Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No.

* Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B PPT No. 17 Biot Savart s Law A straight infinitely long wire is carrying