Magnetism. March 10, 2014 Physics for Scientists & Engineers 2, Chapter 27 1

Size: px
Start display at page:

Download "Magnetism. March 10, 2014 Physics for Scientists & Engineers 2, Chapter 27 1"

Transcription

1 Magnetism March 10, 2014 Physics for Scientists & Engineers 2, Chapter 27 1

2 Notes! Homework is due on We night! Exam 4 next Tuesday Covers Chapters 27, 28, 29 in the book Magnetism, Magnetic Fields, Electromagnetic Induction Material from the week before spring break and this week Homework sets 7 and 8! I will be out of town next week Prof. Joey Huston will teach lectures March 10, 2014 Chapter 29 2

3 Force on a Current Carrying Wire! The magnitude of the magnetic force on a wire of length L carrying a current i is F = il B B F = ilbsinθ! θ is the angle between the current and the magnetic field! Force is perpendicular to both current and magnetic March 10, 2014 Physics for Scientists & Engineers 2, Chapter 27 3

4 Magnetic Field from a Long, Straight Wire! Magnitude: B = µ 0i 2πr! Direction: March 10, 2014 Physics for Scientists & Engineers, Chapter 28 4

5 Magnetic Field due to a Wire Loop! Using more advanced techniques and with the aid of a computer we can determine magnetic field from a wire loop at other points in space March 10, 2014 Physics for Scientists & Engineers, Chapter 28 5

6 Ampere s Law! We have calculated the magnetic field from an arbitrary distribution of current elements using d B = µ 0 4π! We may be faced with a difficult integral! In cases where the distribution of current elements has cylindrical or spherical symmetry, we can apply Ampere s Law to calculate the magnetic field from a distribution of current elements with much less effort than using a direct integration! Ampere s Law is B d s id s r r 3 = µ 0 i enc March 10, 2014 Physics for Scientists & Engineers, Chapter 28 6

7 Ampere s Law! As an example of Ampere s Law, consider the five currents shown below:! The currents are perpendicular to the plane.! We can draw an Amperian loop represented by the red line.! This loop encloses i 1, i 2, and i 3 and excludes i 4 and i 5.! Ampere s Law tells us that: B i d s = µ 0 i 1 + i 2 + i 3 ( ) March 10, 2014 Chapter 28 7

8 Magnetic Fields of Solenoids! Current flowing through a single loop of wire produces a magnetic field that is not very uniform! Applications often require a uniform field! A first step toward a more uniform magnetic field is the Helmholtz coil! This coil consists of 2 sets of coaxial wire loops March 10, 2014 Physics for Scientists & Engineers, Chapter 28 10

9 Magnetic Fields of Solenoids! Let s look at the magnetic field created by 4 coaxial coils! Let s go from 4 coils to many coils March 10, 2014 Physics for Scientists & Engineers, Chapter 28 12

10 Magnetic Fields of Solenoids! Let s look at the magnetic field created by 600 coaxial coils! 600 coils produce an excellent field inside the coils March 10, 2014 Physics for Scientists & Engineers, Chapter 28 13

11 Magnetic Fields of Solenoids! An ideal solenoid has a magnetic field of zero outside and of a uniform constant finite value inside.! To determine the magnitude of the magnetic field inside an ideal solenoid, we can apply Ampere s Law to a section of a solenoid far from its ends.! To do so, we first choose an Amperian loop over which to carry out the integration. March 10, 2014 Chapter 28 14

12 Magnetic Fields of Solenoids! The left hand side of Ampere s Law is: b c d a B i ds = B i ds + B i ds + B i ds + B i ds = Bh a b c d 0 0 Bh! The right hand side of Ampere s Law is: 0 µ0 ienc = µ0 nhi n is the number of turns per unit length! So we get: Bh = µ0 nhi B = µ0 ni March 10, 2014 Chapter 28 15

13 Atoms as Magnets! The atoms that make up all matter contain moving electrons that form current loops that produce magnetic fields.! In most materials, these current loops are randomly oriented and produce no net magnetic field.! In magnetic materials, some of these current loops are naturally aligned.! Other materials can have these current loops aligned by an external magnetic field and become magnetized.! Consider a highly simplified model of an atom. March 10, 2014 Chapter 28 16

14 Atoms as Magnets! Imagine that an atom consists of an electron moving with a constant speed v in a circular orbit with radius r.! We can think of the moving charge of the electron as a current i.! Current is defined as the charge per unit time passing a particular point.! For this case the charge is the charge of the electron e and the time is related to the period of the orbit: i = e T = e ( 2πr)/ v = ve 2πr March 10, 2014 Chapter 28 17

15 Atoms as Magnets! The magnetic moment of the orbiting electron is given by: µ orb = ia = ve 2πr πr 2 = ver 2! We can define the orbital angular momentum of the electron to be: L orb = rp = rmv! Solving and substituting gives us: L orb = rm 2µ orb er = 2mµ orb e March 10, 2014 Chapter 28 18

16 Atoms as Magnets! Rewriting and remembering that the magnetic dipole moment and the angular momentum are vector quantities, we can write: µ orb = e 2m L orb! The negative sign arises because of the definition of current as the flow of positive charge.! This result can be applied to the hydrogen atom, and the correct result is obtained.! However, other predictions of the properties of atoms based on the idea that electrons exist in circular orbits in atoms disagree with experimental observations. March 10, 2014 Chapter 28 19

17 Atoms as Magnets! The magnetic dipole moment from the orbital motion of electrons is not the only contribution to the magnetic moment of atoms.! Electrons and other elementary particles have their own, intrinsic magnetic moments, due to their spin.! The phenomenon of spin will be covered thoroughly in the discussion of quantum physics in Chapters 36 through 39, but some facts about spin and its connection to a particle s intrinsic angular momentum have been discovered experimentally and do not require an understanding of quantum mechanics.! Electrons, protons and neutrons all have spin s = ½. March 10, 2014 Chapter 28 20

18 Atoms as Magnets! The angular momentum of these particles is: ( ) S = s s+1! The z-component of the angular momentum of these particles is: S z = 1 2 or + 1 2! This spin cannot be explained by the orbital motion of some substructure of the particles.! Spin is an intrinsic property, similar to mass or electric charge. March 10, 2014 Chapter 28 21

19 Magnetic Properties of Matter! Magnetic dipoles do not experience a net force in a constant magnetic field.! Magnetic dipoles do experience a net torque in a constant magnetic field.! This torque drives a single free dipole to an orientation with the lowest magnetic potential energy.! What happens when matter is placed in a magnetic field?! The dipole moment of atoms in a material can point in different directions or in the same direction.! The magnetization of a material is defined as the net dipole moment created by the dipole moments of the atoms in the material per unit volume. March 10, 2014 Chapter 28 22

20 Diamagnetism and Paramagnetism! The magnetization depends on the magnetic field strength.! For most materials, but not all, the relationship is linear: M = χ m H! The quantity χ m is the magnetic susceptibility.! There are materials that do not obey this relationship.! The most prominent among those are ferromagnets.! Let s first look at materials that do obey this relationship, diamagnetic and paramagnetic materials.! If χ m < 0, the dipoles in the material tend to arrange themselves to oppose an external magnetic field.! Material with χ m < 0 are diamagnetic. March 10, 2014 Chapter 28 23

21 Diamagnetism! An example of a strawberry exhibiting diamagnetism is shown below! A strawberry being levitated by a strong magnetic field at the High Field Magnet Laboratory, Radboud University Nijmegen, The Netherlands.! Levitating a live frog! In this picture diamagnetic forces induced by a non-uniform external magnetic field of 16 T are levitating a strawberry! The normally negligible diamagnetic force is large enough in this case to overcome gravity October 13, 2008 Physics for Scientists & Engineers 2, Lecture 27 24

22 Paramagnetism! If χ m > 0, the magnetization of the material points in the same direction as the external field.! This property is paramagnetism and materials exhibiting this property are called paramagnetic.! Materials containing certain transition elements, including actinides and rare earths, exhibit paramagnetism.! Each atom of these elements has a permanent magnetic dipole that is normally randomly oriented.! In the presence of an external magnetic field, some of the magnetic dipole moments align with the external field.! When the external field is removed, the induced magnetic dipole moment disappears. March 10, 2014 Chapter 28 25

23 Ferromagnetism! The elements iron, nickel, cobalt, gadolinium and dysprosium and alloys containing these elements exhibit ferromagnetism! Ferromagnetic materials: Long-range ordering at the atomic level Dipole moments of atoms are line up with each other Typically in a limited region called a domain! Within a domain, the magnetic field can be strong! Domains are small and randomly oriented leaving no net magnetic field! An external magnetic field can align these domains and magnetize the material! Iron Ore! Tilden mine, UP March 10, 2014 Chapter 28 26

24 Ferromagnetism (2)! A ferromagnetic material will retain all or some of this induced magnetism when the external magnetic field is removed! The induced magnetic field is in the same direction as the external magnetic field Amplification of magnetic fields, for example inside electromagnets, solenoids or toroids! Demo Insert a ferromagnetic material in the core of a solenoid and see how much the magnetic field is increased March 10, 2014 Chapter 28 27

25 Healing magnets! Can magnets in shoes or worn as bracelets heal people or improve athletic ability?! Superposition principle:! Field is at most 10-4 T at a distance of d=1mm from the magnet center and decreases as 1/d 3! Magnet holder has thickness ~ 5mm, skin thickness ~1mm B field is much less than 10-6 T in muscles and tissue! Much smaller than earth s magnetic field (5*10-5 T)!! And of course the human body is non-magnetic March 10, 2014 Physics for Scientists & Engineers 2, Chapter 27 28

Electricity & Optics

Electricity & Optics Physics 24100 Electricity & Optics Lecture 15 Chapter 27 sec. 3-5 Fall 2016 Semester Professor Koltick Magnetic Fields B = μ 0 4π I dl r r 2 = μ 0 4π I dl r r 3 B = μ 0 2I 4π R B = μ 0 2 IR 2 R 2 + z 2

More information

Magnetic materials, & inductance & Torque. P.Ravindran, PHY041: Electricity & Magnetism 8 February 2013: Magnetic materials, inductance, and torque

Magnetic materials, & inductance & Torque. P.Ravindran, PHY041: Electricity & Magnetism 8 February 2013: Magnetic materials, inductance, and torque Magnetic materials, & inductance & Torque Magnetic Properties of Materials Magnetic behavior of a material is due to the interaction of magnetic dipole moments of its atoms with an external magnetic field.

More information

Magnetic Field Lines for a Loop

Magnetic Field Lines for a Loop Magnetic Field Lines for a Loop Figure (a) shows the magnetic field lines surrounding a current loop Figure (b) shows the field lines in the iron filings Figure (c) compares the field lines to that of

More information

Magnetism. February 27, 2014 Physics for Scientists & Engineers 2, Chapter 27 1

Magnetism. February 27, 2014 Physics for Scientists & Engineers 2, Chapter 27 1 Magnetism February 27, 2014 Physics for Scientists & Engineers 2, Chapter 27 1 Force on a Current Carrying Wire! The magnitude of the magnetic force on a wire of length L carrying a current i is F = il

More information

Physics 202, Lecture 14

Physics 202, Lecture 14 Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch. 27) Review of Biot-Savart Law Ampere s Law Magnetism in Matter Magnetic Fields (Biot-Savart): Summary Current loop, distance on

More information

B for a Long, Straight Conductor, Special Case. If the conductor is an infinitely long, straight wire, θ 1 = 0 and θ 2 = π The field becomes

B for a Long, Straight Conductor, Special Case. If the conductor is an infinitely long, straight wire, θ 1 = 0 and θ 2 = π The field becomes B for a Long, Straight Conductor, Special Case If the conductor is an infinitely long, straight wire, θ 1 = 0 and θ 2 = π The field becomes μ I B = o 2πa B for a Curved Wire Segment Find the field at point

More information

Ch. 28: Sources of Magnetic Fields

Ch. 28: Sources of Magnetic Fields Ch. 28: Sources of Magnetic Fields Electric Currents Create Magnetic Fields A long, straight wire A current loop A solenoid Slide 24-14 Biot-Savart Law Current produces a magnetic field The Biot-Savart

More information

Displacement Current. Ampere s law in the original form is valid only if any electric fields present are constant in time

Displacement Current. Ampere s law in the original form is valid only if any electric fields present are constant in time Displacement Current Ampere s law in the original form is valid only if any electric fields present are constant in time Maxwell modified the law to include timesaving electric fields Maxwell added an

More information

Magnetic Force on a Moving Charge

Magnetic Force on a Moving Charge Magnetic Force on a Moving Charge Electric charges moving in a magnetic field experience a force due to the magnetic field. Given a charge Q moving with velocity u in a magnetic flux density B, the vector

More information

Physics 202, Lecture 14

Physics 202, Lecture 14 Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch 30) Review: The Biot-Savart Law The Ampere s Law Applications And Exercises of ampere s Law Straight line, Loop, Solenoid, Toroid

More information

Physics 202, Lecture 14

Physics 202, Lecture 14 Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch. 30) Review: iot-savart Law, Ampere s Law Displacement Current: Ampere-Maxwell Law Magnetism in Matter Maxwell s Equations (prelude)

More information

DAY 12. Summary of Topics Covered in Today s Lecture. Magnetic Fields Exert Torques on a Loop of Current

DAY 12. Summary of Topics Covered in Today s Lecture. Magnetic Fields Exert Torques on a Loop of Current DAY 12 Summary of Topics Covered in Today s Lecture Magnetic Fields Exert Torques on a Loop of Current Imagine a wire bent into the shape of a rectangle with height h and width w. The wire carries a current

More information

Chapter 27 Sources of Magnetic Field

Chapter 27 Sources of Magnetic Field Chapter 27 Sources of Magnetic Field In this chapter we investigate the sources of magnetic of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents). Ampere s Law

More information

Coaxial cable. Coaxial cable. Magnetic field inside a solenoid

Coaxial cable. Coaxial cable. Magnetic field inside a solenoid Divergence and circulation Surface S Ampere s Law A vector field is generally characterized by 1) how field lines possibly diverge away from or converge upon (point) sources plus 2) how field lines circulate,

More information

Electromagnetic Induction! March 11, 2014 Chapter 29 1

Electromagnetic Induction! March 11, 2014 Chapter 29 1 Electromagnetic Induction! March 11, 2014 Chapter 29 1 Notes! Exam 4 next Tuesday Covers Chapters 27, 28, 29 in the book Magnetism, Magnetic Fields, Electromagnetic Induction Material from the week before

More information

General Physics II. Magnetism

General Physics II. Magnetism General Physics II Magnetism Bar magnet... two poles: N and S Like poles repel; Unlike poles attract. Bar Magnet Magnetic Field lines [B]: (defined in a similar way as electric field lines, direction and

More information

Electromagnetism - Lecture 10. Magnetic Materials

Electromagnetism - Lecture 10. Magnetic Materials Electromagnetism - Lecture 10 Magnetic Materials Magnetization Vector M Magnetic Field Vectors B and H Magnetic Susceptibility & Relative Permeability Diamagnetism Paramagnetism Effects of Magnetic Materials

More information

B r Solved Problems Magnetic Field of a Straight Wire

B r Solved Problems Magnetic Field of a Straight Wire (4) Equate Iencwith d s to obtain I π r = NI NI = = ni = l π r 9. Solved Problems 9.. Magnetic Field of a Straight Wire Consider a straight wire of length L carrying a current I along the +x-direction,

More information

Section 24.8 Magnets and Magnetic Materials Pearson Education, Inc.

Section 24.8 Magnets and Magnetic Materials Pearson Education, Inc. Section 24.8 Magnets and Magnetic Materials A Current Loop in a Uniform Field Slide 24-2 A Current Loop in a Uniform Field A magnetic dipole will rotate to line up with a magnetic field just as an electric

More information

Outside the solenoid, the field lines are spread apart, and at any given distance from the axis, the field is weak.

Outside the solenoid, the field lines are spread apart, and at any given distance from the axis, the field is weak. Applications of Ampere s Law continued. 2. Field of a solenoid. A solenoid can have many (thousands) of turns, and perhaps many layers of windings. The figure shows a simple solenoid with just a few windings

More information

Chapter 29: Magnetic Fields Due to Currents. PHY2049: Chapter 29 1

Chapter 29: Magnetic Fields Due to Currents. PHY2049: Chapter 29 1 Chapter 29: Magnetic Fields Due to Currents PHY2049: Chapter 29 1 Law of Magnetism Unlike the law of static electricity, comes in two pieces Piece 1: Effect of B field on moving charge r r F = qv B (Chapt.

More information

Magnetic field creation (example of a problem)

Magnetic field creation (example of a problem) 1 Magnetic field creation (example of a problem) Three long, straight wires are parallel to each other and perpendicular to the plane of the paper. Their mutual location is shown in Figure below. The currents

More information

The magnetic circuits and fields in materials

The magnetic circuits and fields in materials The magnetic circuits and fields in materials Lecture 14 1 Linear current above a magnetic block In this example, assume a current density J above an infinite slab of linear magnetic material, with permeability,

More information

PHY331 Magnetism. Lecture 1

PHY331 Magnetism. Lecture 1 PHY331 Magnetism Lecture 1 Overview Course syllabus / general information Quick revision of basic concepts Magnetization and susceptibility Using susceptibility to define magnetic materials Diamagnetic

More information

Chapter 28 Sources of Magnetic Field

Chapter 28 Sources of Magnetic Field Chapter 28 Sources of Magnetic Field In this chapter we investigate the sources of magnetic of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents). Ampere s Law

More information

Magnetic field and magnetic poles

Magnetic field and magnetic poles Magnetic field and magnetic poles Magnetic Field B is analogically similar to Electric Field E Electric charges (+ and -)are in analogy to magnetic poles(north:n and South:S). Paramagnetism, Diamagnetism,

More information

Physics 12. Unit 8 Magnetic Field and Electromagnetism Part I

Physics 12. Unit 8 Magnetic Field and Electromagnetism Part I Physics 12 Unit 8 Magnetic Field and Electromagnetism Part I 1. Basics about magnets Magnets have been known by ancient people since long time ago, referring to the iron-rich rocks, called magnetite or

More information

PHYSICS. Chapter 29 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT

PHYSICS. Chapter 29 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 29 Lecture RANDALL D. KNIGHT Chapter 29 The Magnetic Field IN THIS CHAPTER, you will learn about magnetism and the magnetic field.

More information

12:40-2:40 3:00-4:00 PM

12:40-2:40 3:00-4:00 PM PHY294H l Professor: Joey Huston l email:huston@msu.edu l office: BPS3230 l Homework will be with Mastering Physics (and an average of 1 handwritten problem per week) Help-room hours: 12:40-2:40 Monday

More information

Announcements. l LON-CAPA #7 due Wed March 12 and Mastering Physics Chapter 24 due Tuesday March 11 l Enjoy your spring break next week

Announcements. l LON-CAPA #7 due Wed March 12 and Mastering Physics Chapter 24 due Tuesday March 11 l Enjoy your spring break next week Announcements l LON-CAPA #7 due Wed March 12 and Mastering Physics Chapter 24 due Tuesday March 11 l Enjoy your spring break next week hopefully someplace warm Connection with electric currents l The connection

More information

Chapter 28 Sources of Magnetic Field

Chapter 28 Sources of Magnetic Field Chapter 28 Sources of Magnetic Field In this chapter we investigate the sources of magnetic field, in particular, the magnetic field produced by moving charges (i.e., currents), Ampere s Law is introduced

More information

Linear and Nonlinear Magnetic Media (Griffiths Chapter 6: Sections 3-4) Auxiliary Field H We write the total current density flowing through matter as

Linear and Nonlinear Magnetic Media (Griffiths Chapter 6: Sections 3-4) Auxiliary Field H We write the total current density flowing through matter as Dr. Alain Brizard Electromagnetic Theory I (PY 02) Linear and Nonlinear Magnetic Media (Griffiths Chapter 6: Sections -4) Auxiliary Field H We write the total current density flowing through matter as

More information

Lecture 24 Origins of Magnetization (A number of illustrations in this lecture were generously provided by Prof. Geoffrey Beach)

Lecture 24 Origins of Magnetization (A number of illustrations in this lecture were generously provided by Prof. Geoffrey Beach) Lecture 4 Origins of Magnetization (A number of illustrations in this lecture were generously provided by Prof. Geoffrey Beach) Today 1. Magnetic dipoles.. Orbital and spin angular momenta. 3. Non-interacting

More information

Types of Magnetism and Magnetic Domains

Types of Magnetism and Magnetic Domains Types of Magnetism and Magnetic Domains Magnets or objects with a Magnetic Moment A magnet is an object or material that attracts certain metals, such as iron, nickel and cobalt. It can also attract or

More information

(1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule.

(1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule. iclicker Quiz (1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule. a) True b) False Hint: pay attention to how

More information

Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II

Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II Physics 1302W.400 Lecture 33 Introductory Physics for Scientists and Engineering II In today s lecture, we will discuss generators and motors. Slide 30-1 Announcement Quiz 4 will be next week. The Final

More information

Electricity and Magnetism Current Loops and Magnetic Dipoles Magnetism in Matter

Electricity and Magnetism Current Loops and Magnetic Dipoles Magnetism in Matter Electricity and Magnetism Current Loops and Magnetic Dipoles Magnetism in Matter Lana Sheridan De Anza College Mar 5, 2018 Last time magnetic field inside a solenoid forces between current-carrying wires

More information

Chapter 28 Magnetic Fields Sources

Chapter 28 Magnetic Fields Sources Chapter 28 Magnetic Fields Sources All known magnetic sources are due to magnetic dipoles and inherently macroscopic current sources or microscopic spins and magnetic moments Goals for Chapter 28 Study

More information

Exam 3 November 19, 2012 Instructor: Timothy Martin

Exam 3 November 19, 2012 Instructor: Timothy Martin PHY 232 Exam 3 October 15, 2012 Exam 3 November 19, 2012 Instructor: Timothy Martin Student Information Name and section: UK Student ID: Seat #: Instructions Answer the questions in the space provided.

More information

Chapter 22 Magnetism

Chapter 22 Magnetism Chapter 22 Magnetism 1 Overview of Chapter 22 The Magnetic Field The Magnetic Force on Moving Charges The Motion of Charged Particles in a Magnetic Field The Magnetic Force Exerted on a Current-Carrying

More information

Magnetic Fields due to Currents

Magnetic Fields due to Currents Observation: a current of moving charged particles produces a magnetic field around the current. Chapter 29 Magnetic Fields due to Currents Magnetic field due to a current in a long straight wire a current

More information

The initial magnetization curve shows the magnetic flux density that would result when an increasing magnetic field is applied to an initially

The initial magnetization curve shows the magnetic flux density that would result when an increasing magnetic field is applied to an initially MAGNETIC CIRCUITS The study of magnetic circuits is important in the study of energy systems since the operation of key components such as transformers and rotating machines (DC machines, induction machines,

More information

Chapter 6. Magnetostatic Fields in Matter

Chapter 6. Magnetostatic Fields in Matter Chapter 6. Magnetostatic Fields in Matter 6.1. Magnetization Any macroscopic object consists of many atoms or molecules, each having electric charges in motion. With each electron in an atom or molecule

More information

Chapter 16 - Maxwell s Equations

Chapter 16 - Maxwell s Equations David J. Starling Penn State Hazleton PHYS 214 Gauss s Law relates point charges to the value of the electric field. Φ E = E d A = q enc ɛ 0 Gauss s Law relates point charges to the value of the electric

More information

Class 11 : Magnetic materials

Class 11 : Magnetic materials Class 11 : Magnetic materials Magnetic dipoles Magnetization of a medium, and how it modifies magnetic field Magnetic intensity How does an electromagnet work? Boundary conditions for B Recap (1) Electric

More information

Ch 29 - Magnetic Fields & Sources

Ch 29 - Magnetic Fields & Sources Ch 29 - Magnetic Fields & Sources Magnets......are made of ferromagnetic elements: iron, cobalt, nickel, gadolinium... Magnets have a north pole and a south pole. Magnetic Fields 1. The magnetic field

More information

Let's look at the force on a current loop. In a uniform field it is zero: F = I I (dl B) =I I dl B =0 (4) since B is constant and comes outside the in

Let's look at the force on a current loop. In a uniform field it is zero: F = I I (dl B) =I I dl B =0 (4) since B is constant and comes outside the in Midterm: Mean 4.4/30, sigma = 5, high score - 25/30 Topic 3: Magnetostatic Fields in Matter Reading Assignment: Jackson Chapter 5.7-5. The treatment of magnetostatic fields in matter is quite parallel

More information

III.Sources of Magnetic Fields - Ampere s Law - solenoids

III.Sources of Magnetic Fields - Ampere s Law - solenoids Magnetism I. Magnetic Field - units, poles - effect on charge II. Magnetic Force on Current - parallel currents, motors III.Sources of Magnetic Fields - Ampere s Law - solenoids IV.Magnetic Induction -

More information

Handout 8: Sources of magnetic field. Magnetic field of moving charge

Handout 8: Sources of magnetic field. Magnetic field of moving charge 1 Handout 8: Sources of magnetic field Magnetic field of moving charge Moving charge creates magnetic field around it. In Fig. 1, charge q is moving at constant velocity v. The magnetic field at point

More information

PHYS152 Lecture 8. Eunil Won Korea University. Ch 30 Magnetic Fields Due to Currents. Fundamentals of Physics by Eunil Won, Korea University

PHYS152 Lecture 8. Eunil Won Korea University. Ch 30 Magnetic Fields Due to Currents. Fundamentals of Physics by Eunil Won, Korea University PHYS152 Lecture 8 Ch 3 Magnetic Fields Due to Currents Eunil Won Korea University Calculating the Magnetic Field Due to a Current Recall that we had the formula for the electrostatic force: d E = 1 ɛ dq

More information

Sources of Magnetic Field II

Sources of Magnetic Field II Sources of Magnetic Field II Physics 2415 Lecture 18 Michael Fowler, UVa Today s Topics More about solenoids Biot-Savart law Magnetic materials Ampère s Law: General Case Ampère s Law states that for any

More information

Lecture PowerPoints. Chapter 20 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoints. Chapter 20 Physics: Principles with Applications, 6 th edition Giancoli Lecture PowerPoints Chapter 20 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

More information

March 11. Physics 272. Spring Prof. Philip von Doetinchem

March 11. Physics 272. Spring Prof. Philip von Doetinchem Physics 272 March 11 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 32 Summary Magnetic

More information

Electromagnetism - Lecture 12. Ferromagnetism & Superconductivity

Electromagnetism - Lecture 12. Ferromagnetism & Superconductivity Electromagnetism - Lecture 12 Ferromagnetism & Superconductivity Ferromagnetism Hysteresis & Permanent Magnets Ferromagnetic Surfaces Toroid with Ferromagnetic Core Superconductivity The Meissner Effect

More information

Magnetostatics III. P.Ravindran, PHY041: Electricity & Magnetism 1 January 2013: Magntostatics

Magnetostatics III. P.Ravindran, PHY041: Electricity & Magnetism 1 January 2013: Magntostatics Magnetostatics III Magnetization All magnetic phenomena are due to motion of the electric charges present in that material. A piece of magnetic material on an atomic scale have tiny currents due to electrons

More information

Physics 1402: Lecture 18 Today s Agenda

Physics 1402: Lecture 18 Today s Agenda Physics 1402: Lecture 18 Today s Agenda Announcements: Midterm 1 distributed available Homework 05 due Friday Magnetism Calculation of Magnetic Field Two ways to calculate the Magnetic Field: iot-savart

More information

Lecture Outlines Chapter 22. Physics, 3 rd Edition James S. Walker

Lecture Outlines Chapter 22. Physics, 3 rd Edition James S. Walker Lecture Outlines Chapter 22 Physics, 3 rd Edition James S. Walker 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in

More information

Faraday s Law of Induction I

Faraday s Law of Induction I Faraday s Law of Induction I Physics 2415 Lecture 19 Michael Fowler, UVa Today s Topics Magnetic Permeability Faraday s Law of Induction Lenz s Law Paramagnets and Diamagnets Electromagnets Electromagnets

More information

PHYS 1444 Section 501 Lecture #17

PHYS 1444 Section 501 Lecture #17 PHYS 1444 Section 501 Lecture #17 Wednesday, Mar. 29, 2006 Solenoid and Toroidal Magnetic Field Biot-Savart Law Magnetic Materials B in Magnetic Materials Hysteresis Today s homework is #9, due 7pm, Thursday,

More information

Indiana University Physics P332: Electromagnetism Homework #4 (Due Friday 2/15/2019)

Indiana University Physics P332: Electromagnetism Homework #4 (Due Friday 2/15/2019) Indiana University Physics P332: Electromagnetism Homework #4 (Due Friday 2/15/2019) Reading: Griffiths Chapter 6 1. Conceptual Problems 2. Griffiths 6.6 3. Griffiths 6.12 4. Griffiths 6.13 5. Griffiths

More information

Physics 1402: Lecture 17 Today s Agenda

Physics 1402: Lecture 17 Today s Agenda Physics 1402: Lecture 17 Today s Agenda Announcements: Midterm 1 distributed today Homework 05 due Friday Magnetism Trajectory in Constant B Field Suppose charge q enters B field with velocity v as shown

More information

Magnetic Forces and Fields (Chapters 29-30)

Magnetic Forces and Fields (Chapters 29-30) Magnetic Forces and Fields (Chapters 29-30) Magnetism Magnetic Materials and Sources Magnetic Field, Magnetic Force Force on Moving Electric Charges Lorentz Force Force on Current Carrying Wires Applications

More information

Magnetic Forces and Fields

Magnetic Forces and Fields Magnetic Forces and Fields Physics 102 Lecture 3 21 February 2002 IF NOT REGISTERED FOR PHYSICS 102, SEE REGISTRAR ASAP, AND REGISTER 21 Feb 2002 Physics 102 Lecture 3 1 RC Puzzler 21 Feb 2002 Physics

More information

Chapter 29. Magnetic Fields due to Currentss

Chapter 29. Magnetic Fields due to Currentss Chapter 29 Magnetic Fields due to Currentss Refresher: The Magnetic Field Permanent bar magnets have opposite poles on each end, called north and south. Like poles repel; opposites attract. If a magnet

More information

11/13/2018. The Hall Effect. The Hall Effect. The Hall Effect. Consider a magnetic field perpendicular to a flat, currentcarrying

11/13/2018. The Hall Effect. The Hall Effect. The Hall Effect. Consider a magnetic field perpendicular to a flat, currentcarrying The Hall Effect Consider a magnetic field perpendicular to a flat, currentcarrying conductor. As the charge carriers move at the drift speed v d, they will experience a magnetic force F B = ev d B perpendicular

More information

Consider a magnetic field perpendicular to a flat, currentcarrying

Consider a magnetic field perpendicular to a flat, currentcarrying The Hall Effect Consider a magnetic field perpendicular to a flat, currentcarrying conductor. As the charge carriers move at the drift speed v d, they will experience a magnetic force F B = ev d B perpendicular

More information

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

Dr. Todd Satogata (ODU/Jefferson Lab)   Wednesday, March Vector pointing OUT of page Vector pointing IN to page University Physics 227N/232N Ch: 26-27: Magnetism and Magnetic Induction Lab this Friday, Mar 21: Ohms Law and DC RC Circuits So NO QUIZ this Friday!

More information

LECTURE 22 MAGNETIC TORQUE & MAGNETIC FIELDS. Instructor: Kazumi Tolich

LECTURE 22 MAGNETIC TORQUE & MAGNETIC FIELDS. Instructor: Kazumi Tolich LECTURE 22 MAGNETIC TORQUE & MAGNETIC FIELDS Instructor: Kazumi Tolich Lecture 22 2! Reading chapter 22.5 to 22.7! Magnetic torque on current loops! Magnetic field due to current! Ampere s law! Current

More information

1 CHAPTER 12 PROPERTIES OF MAGNETIC MATERIALS

1 CHAPTER 12 PROPERTIES OF MAGNETIC MATERIALS 1 CHAPTER 12 PROPERTIES OF MAGNETIC MATERIALS 12.1 Introduction This chapter is likely to be a short one, not least because it is a subject in which my own knowledge is, to put it charitably, a little

More information

( (Chapter 5)(Magnetism and Matter)

(  (Chapter 5)(Magnetism and Matter) Additional Exercises Question 5.16: Answer the following questions: (a) Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled? (b) Why is diamagnetism,

More information

10/24/2012 PHY 102. (FAWOLE O.G.) Good day. Here we go..

10/24/2012 PHY 102. (FAWOLE O.G.) Good day. Here we go.. Good day. Here we go.. 1 PHY102- GENERAL PHYSICS II Text Book: Fundamentals of Physics Authors: Halliday, Resnick & Walker Edition: 8 th Extended Lecture Schedule TOPICS: Dates Ch. 28 Magnetic Fields 12

More information

Lecture PowerPoints. Chapter 20 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoints. Chapter 20 Physics: Principles with Applications, 6 th edition Giancoli Lecture PowerPoints Chapter 20 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

More information

PHYS 1442 Section 004 Lecture #14

PHYS 1442 Section 004 Lecture #14 PHYS 144 Section 004 Lecture #14 Wednesday March 5, 014 Dr. Chapter 1 Induced emf Faraday s Law Lenz Law Generator 3/5/014 1 Announcements After class pickup test if you didn t Spring break Mar 10-14 HW7

More information

week 8 The Magnetic Field

week 8 The Magnetic Field week 8 The Magnetic Field General Principles General Principles Applications Start with magnetic forces on moving charges and currents A positive charge enters a uniform magnetic field as shown. What is

More information

Lecture 11.2 : Magnetic Force

Lecture 11.2 : Magnetic Force Lecture 11.2 : Magnetic Force Lecture Outline: The Hall Effect Forces on Current-Carrying Wires Forces on Current Loops Magnetic Properties of Matter Textbook Reading: Ch. 32.7-32.10 March 28, 2013 1 Announcements

More information

we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron.

we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron. Physics II we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron. Particle Symbol Charge (e) Mass (kg) Proton P +1 1.67

More information

Electromagnetism II. Cristina Lazzeroni Lecture 5

Electromagnetism II. Cristina Lazzeroni Lecture 5 Electromagnetism II Cristina Lazzeroni c.lazzeroni@bham.ac.uk Lecture 5 Maxwell s equations for free space They apply simultaneously at any given point in free space. How do they change in presence of

More information

CHAPTER 2 MAGNETISM. 2.1 Magnetic materials

CHAPTER 2 MAGNETISM. 2.1 Magnetic materials CHAPTER 2 MAGNETISM Magnetism plays a crucial role in the development of memories for mass storage, and in sensors to name a few. Spintronics is an integration of the magnetic material with semiconductor

More information

Sources of Magnetic Field

Sources of Magnetic Field Chapter 28 Sources of Magnetic Field PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Learning Goals for Chapter 28 Looking forward

More information

For the rotation around the symmetry axis z as shown on the figure 5.65, the moment of inertial of the thin toroid is I = MR 2, (1)

For the rotation around the symmetry axis z as shown on the figure 5.65, the moment of inertial of the thin toroid is I = MR 2, (1) PHY 352 K. Solutions for problem set #11. Problem 5.58: (a) It does not matter if the rotating object on figure 5.65 is a donut, or a ring, or any other kind of a toroid, as long as it s thin compared

More information

MAGNETIC PROBLEMS. (d) Sketch B as a function of d clearly showing the value for maximum value of B.

MAGNETIC PROBLEMS. (d) Sketch B as a function of d clearly showing the value for maximum value of B. PHYS2012/2912 MAGNETC PROBLEMS M014 You can investigate the behaviour of a toroidal (dough nut shape) electromagnet by changing the core material (magnetic susceptibility m ) and the length d of the air

More information

Chapter 22: Magnetism

Chapter 22: Magnetism Chapter 22: Magnetism Magnets Magnets are caused by moving charges. Permanent Magnets vs. Electromagnets Magnets always have two poles, north and south. Like poles repel, opposites attract. Brent Royuk

More information

Sources of Magnetic Field

Sources of Magnetic Field Chapter 28 Sources of Magnetic Field PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 28 To determine the

More information

Magnetic Forces and Fields (Chapters 32)

Magnetic Forces and Fields (Chapters 32) Magnetic Forces and Fields (Chapters 32) Magnetism Magnetic Materials and Sources Magnetic Field, B Magnetic Force Force on Moving Electric Charges Lorentz Force Force on Current Carrying Wires Applications

More information

Chapter 22: Magnetism. Brent Royuk Phys-112 Concordia University

Chapter 22: Magnetism. Brent Royuk Phys-112 Concordia University Chapter 22: Magnetism Brent Royuk Phys-112 Concordia University Magnets Magnets are caused by moving charges. Permanent Magnets vs. Electromagnets Magnets always have two poles, north and south. Like poles

More information

PHY331 Magnetism. Lecture 3

PHY331 Magnetism. Lecture 3 PHY331 Magnetism Lecture 3 Last week Derived magnetic dipole moment of a circulating electron. Discussed motion of a magnetic dipole in a constant magnetic field. Showed that it precesses with a frequency

More information

Electromagnetism. Chapter I. Figure 1.1: A schematic diagram of Earth s magnetic field. Sections 20-1, 20-13

Electromagnetism. Chapter I. Figure 1.1: A schematic diagram of Earth s magnetic field. Sections 20-1, 20-13 Chapter I Electromagnetism Day 1 Magnetism Sections 20-1, 20-13 An investigation of permanent magnets shows that they only attract certain metals specifically those containing iron, or a few other materials,

More information

Phys 102 Lecture 11 Magnetic dipoles & current loops

Phys 102 Lecture 11 Magnetic dipoles & current loops Phys 102 Lecture 11 Magnetic dipoles & current loops 1 Today we will... Learn how magnetic fields act on Magnetic dipoles Current loops Apply these concepts! Magnetotactic bacteria Principles behind NMR/MRI,

More information

Transformed E&M I homework. Auxiliary Field Linear and Nonlinear Media (Griffiths Chapter 6)

Transformed E&M I homework. Auxiliary Field Linear and Nonlinear Media (Griffiths Chapter 6) Transformed E&M I homework Auxiliary Field Linear and Nonlinear Media (Griffiths Chapter 6) Auxiliary field H Question 1. Coaxial cylinders separated by magnetic material Pollack and Stump, 9-15 pg. 352

More information

Magnetic Materials. 1. Magnetization 2. Potential and field of a magnetized object

Magnetic Materials. 1. Magnetization 2. Potential and field of a magnetized object Magnetic Materials 1. Magnetization 2. Potential and field of a magnetized object 3. H-field 4. Susceptibility and permeability 5. Boundary conditions 6. Magnetic field energy and magnetic pressure 1 Magnetic

More information

Geophysics 223 January Geophysics 223 C1: Basics of Geomagnetism. C1.1 Introduction

Geophysics 223 January Geophysics 223 C1: Basics of Geomagnetism. C1.1 Introduction Geophysics 223 C1: Basics of Geomagnetism C1.1 Introduction Lodestone was known to the Greeks (800 BC) and Chinese (300 BC) First compass (200 BC) made by Chinese, but not clear why it worked Europeans

More information

Creating Energy-Level Diagrams Aufbau (building up) Principle Electrons are added to the lowest energy orbital available.

Creating Energy-Level Diagrams Aufbau (building up) Principle Electrons are added to the lowest energy orbital available. 3.6 Atomic Structure and the Periodic Table Bohr's Theory Was Incorrect Because... Only explained the line spectrum of hydrogen Position and motion of an e cannot be specified (since the e is so small,

More information

General Physics II. Magnetic Fields and Forces

General Physics II. Magnetic Fields and Forces General Physics II Magnetic Fields and Forces 1 Magnetism Magnetism underlies the operation of the hard disk drive, which is the mainstay of modern electronic information storage, from computers to ipods.

More information

Chapter 7 Magnetism 7.1 Introduction Magnetism has been known thousands of years dating back to the discovery recorded by the ancient Greek.

Chapter 7 Magnetism 7.1 Introduction Magnetism has been known thousands of years dating back to the discovery recorded by the ancient Greek. Chapter 7 Magnetism 7.1 Introduction Magnetism has been known thousands of years dating back to the discovery recorded by the ancient Greek. 1900 Maxwell combine the theory of electric and magnetic to

More information

Lecture 36: WED 19 NOV CH32: Maxwell s Equations II

Lecture 36: WED 19 NOV CH32: Maxwell s Equations II Physics 2113 Jonathan Dowling Lecture 36: WED 19 NOV CH32: Maxwell s Equations II James Clerk Maxwell (1831-1879) Maxwell s Displacement Current B E B If we are charging a capacitor, there is a current

More information

Torque on a Current Loop

Torque on a Current Loop Today Chapter 19 Magnetism Torque on a current loop, electrical motor Magnetic field around a current carrying wire. Ampere s law Solenoid Material magnetism Clicker 1 Which of the following is wrong?

More information

Solid State Physics MAGNETISM I. Lecture 27. A.H. Harker. Physics and Astronomy UCL

Solid State Physics MAGNETISM I. Lecture 27. A.H. Harker. Physics and Astronomy UCL Solid State Physics MAGNETISM I Lecture 27 A.H. Harker Physics and Astronomy UCL 10 Magnetic Materials Magnet technology has made enormous advances in recent years without the reductions in size that have

More information

μ 0 I enclosed = B ds

μ 0 I enclosed = B ds Ampere s law To determine the magnetic field created by a current, an equation much easier to use than Biot-Savart is known as Ampere s law. As before, μ 0 is the permeability of free space, 4π x 10-7

More information

Chapter 30 Sources of the magnetic field

Chapter 30 Sources of the magnetic field Chapter 30 Sources of the magnetic field Force Equation Point Object Force Point Object Field Differential Field Is db radial? Does db have 1/r2 dependence? Biot-Savart Law Set-Up The magnetic field is

More information

Fundamental Constants

Fundamental Constants Fundamental Constants Atomic Mass Unit u 1.660 540 2 10 10 27 kg 931.434 32 28 MeV c 2 Avogadro s number N A 6.022 136 7 36 10 23 (g mol) 1 Bohr magneton μ B 9.274 015 4(31) 10-24 J/T Bohr radius a 0 0.529

More information