Magnetic Forces and Fields (Chapters 32)
|
|
- Jayson Leonard
- 5 years ago
- Views:
Transcription
1 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 Electromagnetic motors Torques on magnetic dipole moments µ Sources of Magnetic Field Magnetic field of a moving charge Current Carrying Wires Biot-Savart law Loops, Coils and Solenoids Ampère s Law Microscopic Nature of Magnetism
2 Magnetism Magnets and relation to electricity Magnets are objects exhibiting magnetic behavior or magnetism A magnet exhibits the strongest magnetism at extremities called magnetic poles: any magnet has two poles, conventionally dubbed north and south Like poles repel each other and unlike poles attract each other Unlike charges, magnetic poles cannot be isolated into monopoles: if a permanent magnetic is cut in half repeatedly, the parts will still have a north and a south pole How can one magnetize objects? Magnetism can be induced: either by stroking an unmagnetized piece of magnetizable material with a magnet, or by placing it near a strong permanent magnet Soft magnetic materials, such as iron, are easily magnetized - They also tend to lose their magnetism easily Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize - They tend to retain their magnetism The region of space surrounding a moving charge includes a magnetic field as well as by an electric field: so, magnetism and electricity cannot be separated They are interrelated into the integrated field of electromagnetism: the first breakthrough in the great effort of developing unified theories about fundamental interactions (Maxwell, beginning of the XX-th century).
3 Magnetic Field Operational definition and field lines Like the sources of electric field, any magnetic material produces a magnetic field that surrounds it and extends to infinity. The symbol used to represent this vector is Let s first describe this vector using an operational definition: Def: The magnetic field in each location in the surroundings of a magnetic source is a vector with the direction given by the direction of the north pole of a compass needle placed in the respective location Similar to the electric field, a magnetic field can be patterned using field lines: the vector B in a point is tangent to the line passing through that point, and the density of lines represents the strength of the field However, while electric field lines start and end on electric charges (electric monopoles), the magnetic field lines form closed loops (since there are no magnetic monopoles) Thus, the magnetic field lines should be seen as closing the loops through the body of the magnet: that is, the magnetic field inside magnets is not zero B Ex: A compass can be used to trace the magnetic field lines
4 Magnetic Field Magnetic field lines for various magnetic sources A compass can be used to probe the magnetic field lines produced by various source, and they will always form closed loops Later we ll look at these sources more systematically: otice the similar pattern
5 Magnetic Field Example: Earth s Magnetic Field The Earth s geographic north pole is closed to a (slowly migrating) magnetic south pole The Earth s magnetic field resembles that of a huge bar magnet deep in the Earth s interior slightly tilted with respect to the axis of rotation of the planet The mechanism of Earth s magnetism is not very well understood There cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetization The most likely source is believed to be electric currents in the liquid part of the planetary core The direction of the Earth s magnetic field reverses every few million years The origin of the reversals is not well understood in detail, albeit there are models describing how it may happen
6 Magnetic Force On a moving charge Magnetic fields act on moving charges with magnetic forces. We ll study this effect in two (related) cases: 1. Moving Charged Particles F 2. Current Carrying Wires 1. Magnetic Force on a Moving Point Charge Consider a test charge q moving in a field B with velocity v making an angle θ with B: the particle will be acted by a magnetic force F (sometimes called Lorentz force) of Magnitude: F = qv B F = qvb sinθ Direction: given by a right hand rule (let s call it #1): The expression for the magnetic force leads to a definition for magnetic field unit called Tesla (T) N B = Tesla (T) = S C m s A popular alternative is the cgs unit, Gauss (G) (useful for small fields): 1T = 10 4 Gauss v B θ B v q>0 F q>0 F q<0
7 otation: Vectors perpendicular on page/board/slide: Outward nward Exercises: 1. Force direction: Find the direction of the force on an electron moving through the magnetic fields represented below. 2. Field direction: Find the direction of the magnetic field acting on a proton moving as represented by the adjacent velocity and force vectors. (Assume that the velocity is perpendicular on the magnetic field.) Problem: 1. Charge moving in a magnetic field: What velocity would a proton need to circle Earth 800 km above the magnetic equator, where Earth's magnetic field is directed horizontally north and has a magnitude of T?
8 Magnetic Force Charge in an electromagnetic field Any moving charge not only that is acted by a magnetic field but it also produces a magnetic field that surrounds it and extends to infinity A test charge q moving in an electric field E and a magnetic field B, with velocity making an angle θ with B will be acted by a net electromagnetic force (sometimes called Lorentz force): F = F + F = q + v electric magnetic ( E B) parallel to the direction of E perpendicular on the direction of B + Ex: One type of velocity selector Consider an electric field perpendicular on a magnetic field Then only the particles entering the fields with velocity perpendicular of both will be allowed to pass, which corresponds to the following condition that the particles are supposed to obey: E qe+ qvb= 0 v= B +
9 Magnetic Force Trajectory of a point charge in a magnetic field Let s look at two particular trajectories that a charged B particle may have in a magnetic field 1. Consider a particle moving into an external magnetic field so that its velocity is perpendicular to the field n this case, the particle will move in a circle, with the magnetic force always directed toward the center of the circular path Equating the magnetic and centripetal forces, we can find the radius of the circle: 2 v F = qvb= m r mv qb 2. f the particle s velocity is not perpendicular to the field, the path followed by the particle is a spiral called a helix The helix spirals along the direction of the field with a velocity given by the component of the velocity parallel with B r = : called cyclotron equation v + + F + F v F + v v
10 Magnetic Force Currents in magnetic field A current is a collection of many drifting charged particles, such that a magnetic force is expected to act on a current-carrying wire placed in a magnetic field This magnetic force is the resultant of the forces acted on the individual microscopic electric carriers, but it makes more sense to integrate its effects into a unique magnetic force acted on the macroscopic current = 0 F = 0 F F Ex: Experimental observations: A current carrying vertical wire placed in a magnetic field pointing perpendicular into the slide, will be acted by a magnetic force perpendicular on the current and magnetic field: either to the left, or to the right, depending on the direction of the current
11 2. Magnetic Force on Current Carrying Wire Consider a straight current carrying wire of length l immersed in field B, making an angle θ with B: the portion dl of wire will be acted by a magnetic force df Magnitude: df Magnetic Force On a current carrying wire df = dl B = Bdlsinθ Direction: Given by right hand rule #1, but instead of aligning the fingers with the velocity, one aligns the fingers with the direction of the current Since the current flows in the direction of the positive carriers, the thumbs always indicates the direction of the force f the wire is straight, and the force is the same for each cross-section, the force on a length L of wire is F BLsinθ = B B θ F F d l
12 Problems: 2. Basics of a rail gun: A rail gun looks (very)schematically as in the figure. Evaluate the speed that the projectile of mass m would achieve after traveling from rest a distance d on the rails spaced by l with a driving current with a magnetic field B. Rail B m Projectile l 3. Force on a semicircular current: A semicircular thin conductor of radius a carries a time dependent current i = t e τ 0, where 0 and τ are positive constant. The wire is allowed to move vertically through a uniform magnetic field B, as in the figure. Find the acceleration of the conductor as a time dependent function. R a y B a θ i x
13 Applications Torque on a Current Loop The magnetic force can be used to make electromagnetic motors by using it to rotate a current carrying loops n order to see the principles of such an arrangement, consider a loop carrying a current in an external magnetic field B The two sides perpendicular on B will be acted by forces opposite in direction creating a torque that will rotate the loop: 1 τ = F a θ sin τ = F 2 asinθ+ F 2 asinθ = F 2 asinθ F = Bb angle between the magnetic field and the perpendicular to the surface of the loop 1 2 = F2 2 asin We can immediately find an expression for the net torque τ = τ 1 + τ 2 : τ τ = Bba sinθ = BAsinθ We see that the torque is maximum when the magnetic field B is parallel with the plane of area A (θ = 90 ), and zero when B is perpendicular on A (θ = 0 ) θ F F
14 Magnetic Moment, µ The net torque exerted by a magnetic field on current carrying loops is τ = ABsinθ This magnetic torque exerted on the loop of current can be written in terms of a vector quantity called magnetic moment: τ = µ B τ = µ Bsinθ Any loop of electric current can be associated with a magnetic moment pointing perpendicular on the plane of the loop So, we see that a magnetic dipole in a magnetic field will have the tendency to rotate either in a position with µ parallel with B stable equilibrium or anti-parallel with B unstable equilibrium The current doesn t have to be carried by a wire: any closed loop of moving charges will have a moment: as we shall see later, these moments explain magnetism at a microscopic scale Ex: Electrons in an atom have an orbital moment due to the their orbital motion about the nucleus µ= A +
15 Applications Electromagnetic Motors An electric motor converts electrical energy into mechanical energy in the form of rotational kinetic energy As described on the previous slides, the simplest electric motor consists of a rigid current-carrying loop that rotates when placed in a magnetic field The torque acting on the loop will tend to rotate the loop to smaller values of θ until the torque becomes 0 at θ = 0 f the loop turns past this point and the current remains in the same direction, the torque reverses and turns the loop in the opposite direction To provide continuous rotation in one direction, the current in the loop must periodically reverse, such that dc-motors must use split-ring commutators and brushes Actual motors would contain many current loops and commutators
16 Sources of Magnetic Field Moving Charge We ve seen that magnetic fields act on moving charges (point-like and currents), so it is just natural to expect that moving charges also produce magnetic fields: a fact first discovered serendipitously by Hans Oersted in 1819 Consider a point charge moving with constant velocity v: then, the magnetic field B at a position r from the particle making an angle θ with v is B= µ ˆ 0 qv r 2 4π r where µ -7 0 = 4 π 10 Tm/A is the magnetic permeability of free space Magnitude: B = µ 0 4π q vsinθ Direction: perpendicular on the plane determined by r and v. Use the following right hand rule (#2): grab the velocity in your right hand with the thumb in its direction. Then the curl of the fingers will show the direction of the field around v: clockwise for positive charges and anticlockwise for negative charges r 2 Weaker field behind + r θ v Larger field in the plane B + B B Weaker fields ahead B v
17 Problem: 4. Moving charges interacting electrically and magnetically: Two protons move with uniform speed v along parallel paths at distance r from each other. a) Find a symbolical expression for the magnetic force exerted by one proton on the other one: is it attractive or repulsive? s this always the case? b) Calculate the electric force between the charges and compare to the magnetic force. + +
18 Sources of Magnetic Field Element of current Consider a current carried along a wire. Then, the magnetic field produced by a segment dl of the current at a position r from the segment making an angle φ with dl is given by Magnitude: Biot-Savart Law: db= db = µ ˆ 0 d l r 2 4π r µ 0 dlsinϕ 2 4π r Direction: perpendicular on the plane determined by r and v. Use the same right hand rule as for moving positively charged particles, but curl your right hand fingers around the current. Hence, for a certain finite length of wire B µ 0 = 4π d l rˆ 2 r db d l db r φ db db db
19 Problems: 5. Straight Current: A straight wire of length 2a centered in y = 0, carries a current in positive y-direction. Calculate the magnetic field at distance r along x-axis. Useful integral: a a dy y 2a = = ( x + y ) x( x + y ) x( x + a ) a a 6. Circular Current: A circular wire loop of radius a lays in the yz-plane and is traveled by counterclockwise current. a) Calculate the magnetic field produced at a distance x along the axis of the loop. b) Using the result, find the field in the center of the ring.
20 Sources of Magnetic Fields Long straight wire Consider a long straight wire carrying a current, the magnetic field at a distance r perpendicular on the wire is given by: Magnitude: using the result for Problem 5: µ 0 1 B= a π r r a + 1 Direction: Given by the right hand rule #2 Comments: The magnetic field has cylindrical symmetry around the wire t gets weaker and weaker as the circles are larger and larger B = µ 0 2π r Quiz 1: A long wire carries a current as in the figure. Compared to the magnetic field at point A, the magnetic field at point B is a) Half as strong, same direction. b) Half as strong, opposite direction. c) One-quarter as strong, same direction. d) One-quarter as strong, opposite direction.
21 Magnetic Force Between Two Parallel Conductors f two long current carrying wires are placed parallel with each other, they will interact via magnetic forces The force on wire 1 is due to magnetic field produced by wire 2 onto the current in 1, so the force per unit length L is: Comments: = B = µ 2π r F L 0 L µ 0 2π r Parallel currents attract each other whereas anti-parallel conductors repel each other F L = The force between parallel conductors can be used to redefine the Ampere (A) Def: f two long, parallel wires 1 m apart carry the same current, and the magnitude of the magnetic force per unit length is 2 x 10-7 N/m, then the current is defined to be 1 A Then the Coulomb (C) can be also defined in terms of the Ampere Def: f a conductor carries a steady current of 1 A, then the quantity of charge that flows through any cross section in 1 second is 1 C
22 Problems: 7. Force on a moving particle by a current carrying wire: A proton moves with speed v = 0.25 m/s parallel with a long wire carrying a current = 2.0 A, at distance r = 1.0 mm. Calculate the magnetic force on the proton. r + v e + 8. Superposition of aligned magnetic fields: Two long parallel wires carry currents 1 and 2 in opposite directions. The figure is an end view of the conductors. Calculate the magnitudes of the magnetic field in points A, B and C located at given equal distances a from the closest wires. A 1 B 2 C a a a a
23 Sources of Magnetic Fields Circular loop of current. Coils f we allow x 0 in the result of Problem 6, the magnetic field in the center of a circular loop is B 2 µ µ 0 a µ B= x= 0 B= 2 x + a ( ) 2a Notice that a current loop can be seen as a magnet with magnetic field lines that remind of the equipotential lines of an electric dipole: so the loop behaves like a magnetic dipole loops form a coil with the maximum field in the middle of the coil: S The field produced by a loop or a coil is related to the respective magnetic moment µ Ex: Magnetic field and moment: the magnetic field in the center of a circular loop is related to its magnetic moment as given by µ = π a = 0 Bmax = a µ 2 0 B 3 2 a µ π µ 2 B The magnetic field B inside has the same direction as the magnetic moment µ
24 Magnetism in Materials Magnetic moments of electrons Now we are prepared to see that the magnetism of materials is microscopically mainly determined by the alignment of elementary electronic magnetic dipoles Notice first that atoms should act like magnets because of the orbital motion of the electrons about the nucleus Since each electron circles the atom once in about every seconds, it produces a current of 1.6 ma and a magnetic field of about 20 T at the center of the orbit However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom, so the net result is that the magnetic effect produced by electrons orbiting the nucleus is either zero or very small for most materials The classical model is to consider the electrons to spin like tops but it is actually a quantum effect. The magnetic moment of an electron is given by Bohr magneton: µ B = J T Most materials are not naturally magnetic since electrons usually pair up with their spins opposite each other + µ spin
25 Paramagnets Magnetism in Materials Types of magnetism So, since the alignment of elementary magnetic dipoles associated with the electronic spins depends on the microscopic structure, various materials are classified depending on how they behave in external magnetic fields: Ex: aluminum, uranium Moments point in random directions in zero external field but in an external field B ext they rotate so the net field increases The increment in field is small and paramagnetism competes with thermal motion Ferromagnets Ex: iron, nickel n some materials, large groups of atoms in which the spins are aligned form ferromagnetic domains When an external field B ext is applied, the domains that are aligned with the field tend to grow at the expense of the others This causes the material to become magnetized by amounts larger than in the paramagnetic case The magnetization is slowly disappearing after removing the external field Diamagnets Ex: mercury, superconductors, animal bodies n these materials an external magnetic field induces opposite magnetic n these cases the internal magnetic field is less than the external one A diamagnet placed in an external magnetic field will have the tendency to float B ext B ext
26 Ampère s Law André-Marie Ampère found a procedure for deriving the relationship between the current in an arbitrarily shaped wire and the magnetic field produced by the wire: Ampère s Circuital Law: f a net current encl is enclosed by an arbitrary closed path, the integral of all products B dl (where B is the component of the magnetic field along each elementary step dl of the path) is proportional to encl : B dl=µ 0 encl 3 d l Amperian loop B B B Line integral around a closed path called an Amperian loop et current inside the path Ex: Ampere s law can be used to demonstrate the result that we obtained previously for a closed circular path around a long straight current : since the circumference of the path is 2π r, and by symmetry the field around the Amperian is expected to be everywhere constant and tangent to the path, we get: B dl= B dl= B2π r= µ B= 0 encl µ 0 2π r encl = B r
27 Problem: 8. Magnetic field inside and outside of a current carrying conductor: A cylindrical conductor with radius R carries a current uniformly distributed over the cross-sectional area of the conductor. Confirm the relationships given below for the magnetic field in the interior and the exterior of the conductor.
28 Sources of Magnetic Field Solenoids f a long straight wire is wound into B a coil of closely spaced loops, the resulting device is called a solenoid t is also known as an electromagnet since it acts like a magnet only when it carries a current Direction The field lines of the solenoid resemble those of a bar magnet and the field direction is given by the right hand rule applied to the current through any of the turns Magnitude The magnitude of the field inside a solenoid is constant at all points far from its ends B= nµ where n is the number of turns per unit length This expression can be obtained by applying Ampère s Law to the solenoid 0 n = l S solenoid S bar magnet Quiz 2: What is the direction of the field in the center of the solenoid below?
29 Sources of Magnetic Field Solenoid field using Ampère s Law Consider a cross-sectional view of a tightly wound solenoid of turn density n, carrying a current f the solenoid is long compared to its radius, we assume the field inside is uniform and outside is zero Then we can apply Ampère s Law to a rectangular Amperian a b c d a: Amperian loop with turns inside Comment: n reality the field is not perfectly uniform along the axis of a cylinder. BL= µ 0 B= µ 0 = nµ 0 L Ampère s law
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 informationChapter 21. Magnetism
Chapter 21 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
More informationTorque 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 informationCHAPTER 20 Magnetism
CHAPTER 20 Magnetism Units Magnets and Magnetic Fields Electric Currents Produce Magnetic Fields Force on an Electric Current in a Magnetic Field; Definition of B Force on Electric Charge Moving in a Magnetic
More informationChapter 22, Magnetism. Magnets
Chapter 22, Magnetism Magnets Poles of a magnet (north and south ) are the ends where objects are most strongly attracted. Like poles repel each other and unlike poles attract each other Magnetic poles
More informationKirchhoff s rules, example
Kirchhoff s rules, example Magnets and Magnetism 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
More informationChapter 19. Magnetism
Chapter 19 Magnetism The figure shows the path of a negatively charged particle in a region of a uniform magnetic field. Answer the following questions about this situation (in each case, we revert back
More informationB 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 informationMagnetic 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 informationPhysics 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 informationPHYSICS. 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 informationGravity Electromagnetism Weak Strong
19. Magnetism 19.1. Magnets 19.1.1. Considering the typical bar magnet we can investigate the notion of poles and how they apply to magnets. 19.1.1.1. Every magnet has two distinct poles. 19.1.1.1.1. N
More informationCh. 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 informationChapter 30. Sources of the Magnetic Field Amperes and Biot-Savart Laws
Chapter 30 Sources of the Magnetic Field Amperes and Biot-Savart Laws F B on a Charge Moving in a Magnetic Field Magnitude proportional to charge and speed of the particle Direction depends on the velocity
More informationChapter 19. Magnetism. 1. Magnets. 2. Earth s Magnetic Field. 3. Magnetic Force. 4. Magnetic Torque. 5. Motion of Charged Particles. 6.
Chapter 19 Magnetism 1. Magnets 2. Earth s Magnetic Field 3. Magnetic Force 4. Magnetic Torque 5. Motion of Charged Particles 6. Amperes Law 7. Parallel Conductors 8. Loops and Solenoids 9. Magnetic Domains
More informationSo far. Chapter 19. Today ( ) Magnets. Types of Magnetic Materials. More About Magnetism 10/2/2011
So far Chapter 19 Magnetism Electrostatics, properties of stationary charges Coulomb s law Electric field, electric potential Capacitors Ohm s law and resistance Today (19.1-19.4) Magnets Magnetism Earth
More informationChapter 29. Magnetic Fields
Chapter 29 Magnetic Fields A Brief History of Magnetism 13 th century BC Chinese used a compass Uses a magnetic needle Probably an invention of Arabic or Indian origin 800 BC Greeks Discovered magnetite
More informationGeneral 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 informationChapter 19. Magnetism
Chapter 19 Magnetism Magnetic Fields When moving through a magnetic field, a charged particle experiences a magnetic force This force has a maximum value when the charge moves perpendicularly to the magnetic
More informationChapter 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 informationChapter 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 informationPHY 1214 General Physics II
PHY 1214 General Physics II Lecture 15 Magnetic Fields and Forces June 28, 2005 Weldon J. Wilson Professor of Physics & Engineering Howell 221H wwilson@ucok.edu Lecture Schedule (Weeks 4-6) We are here.
More informationChapter 29. Magnetic Fields
Chapter 29 Magnetic Fields Outline 29.1 Magnetic Fields and Forces 29.2 Magnetic Force Acting on a Current-Carrying Conductor 29.4 Motion of a Charged Particle in a Uniform Magnetic Field 29.5 Applications
More informationChapter 27, 28 & 29: Magnetism & Electromagnetic Induction
Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction 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 informationElectromagnetism. 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 informationMagnetism. Permanent magnets Earth s magnetic field Magnetic force Motion of charged particles in magnetic fields
Magnetism Permanent magnets Earth s magnetic field Magnetic force Motion of charged particles in magnetic fields Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
More informationMagnetic 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 informationChapter 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 informationMagnetic Fields and Forces
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 20 Magnetic Fields and Forces Marilyn Akins, PhD Broome Community College Magnetism Magnetic fields are produced by moving electric charges
More informationChapter 21. Magnetic Forces and Magnetic Fields
Chapter 21 Magnetic Forces and Magnetic Fields 21.1 Magnetic Fields The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.
More informationSome History of Magnetism
Magnetism Some History of Magnetism The ancient Greeks were the first to observe magnetism. They studied the mineral magnetite. The poles of a magnet were observed to be south or north seeking. These properties
More informationKey Contents. Magnetic fields and the Lorentz force. Magnetic force on current. Ampere s law. The Hall effect
Magnetic Fields Key Contents Magnetic fields and the Lorentz force The Hall effect Magnetic force on current The magnetic dipole moment Biot-Savart law Ampere s law The magnetic dipole field What is a
More informationMagnetic 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 informationChapter 19. Magnetsm
Chapter 19 Magnetsm Quiz 6. 1. The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic (a) attracted, (b) repelled, or (c) unaffected by the magnet?
More information10/24/2012 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 informationMagnetic Force. A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?
Magnetic Force A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire? (a) left (b) right (c) zero (d) into the page (e) out of the page B
More informationPhysics 202, Lecture 11
Physics 202, Lecture 11 Today s Topics Magnetic Fields and Forces (Ch. 27) Magnetic materials Magnetic forces on moving point charges Magnetic forces on currents, current loops Motion of charge in uniform
More informationChapter 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 informationMay 08, Magnetism.notebook. Unit 9 Magnetism. This end points to the North; call it "NORTH." This end points to the South; call it "SOUTH.
Unit 9 Magnetism This end points to the North; call it "NORTH." This end points to the South; call it "SOUTH." 1 The behavior of magnetic poles is similar to that of like and unlike electric charges. Law
More informationMagnetic Fields Permanent Magnets
1 Magnetic Fields Permanent Magnets Magnetic fields are continuous loops leaving a North pole and entering a South pole they point in direction that an isolated North would move Highest strength near poles
More information> What happens when the poles of two magnets are brought close together? > Two like poles repel each other. Two unlike poles attract each other.
CHAPTER OUTLINE Section 1 Magnets and Magnetic Fields Key Idea questions > What happens when the poles of two magnets are brought close together? > What causes a magnet to attract or repel another magnet?
More informationMagnetic Fields. or I in the filed. ! F = q! E. ! F = q! v! B. q! v. Charge q as source. Current I as source. Gauss s Law. Ampere s Law.
Magnetic Fields Charge q as source Gauss s Law Electric field E F = q E Faraday s Law Ampere-Maxwell Law Current I as source Magnetic field B Ampere s Law F = q v B Force on q in the field Force on q v
More informationPhysics / Higher Physics 1A. Electricity and Magnetism Revision
Physics / Higher Physics 1A Electricity and Magnetism Revision Electric Charges Two kinds of electric charges Called positive and negative Like charges repel Unlike charges attract Coulomb s Law In vector
More informationTridib s Physics Tutorials. NCERT-XII / Unit- 4 Moving charge and magnetic field
MAGNETIC FIELD DUE TO A CURRENT ELEMENT The relation between current and the magnetic field, produced by it is magnetic effect of currents. The magnetic fields that we know are due to currents or moving
More informationMAGNETIC 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 informationMagnetic 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 informationMagnetic 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 informationCHETTINAD COLLEGE OF ENGINEERING & TECHNOLOGY NH-67, TRICHY MAIN ROAD, PULIYUR, C.F , KARUR DT.
CHETTINAD COLLEGE OF ENGINEERING & TECHNOLOGY NH-67, TRICHY MAIN ROAD, PULIYUR, C.F. 639 114, KARUR DT. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL Subject Name: Electromagnetic
More informationPhysics 202, Lecture 13. Today s Topics. Magnetic Forces: Hall Effect (Ch. 27.8)
Physics 202, Lecture 13 Today s Topics Magnetic Forces: Hall Effect (Ch. 27.8) Sources of the Magnetic Field (Ch. 28) B field of infinite wire Force between parallel wires Biot-Savart Law Examples: ring,
More informationDAY 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 informationChapter 28. Magnetic Fields. Copyright 2014 John Wiley & Sons, Inc. All rights reserved.
Chapter 28 Magnetic Fields Copyright 28-2 What Produces a Magnetic Field? 1. Moving electrically charged particles ex: current in a wire makes an electromagnet. The current produces a magnetic field that
More informationn Higher Physics 1B (Special) (PHYS1241) (6UOC) n Advanced Science n Double Degree (Science/Engineering) n Credit or higher in Physics 1A
Physics in Session 2: I n Physics / Higher Physics 1B (PHYS1221/1231) n Science, dvanced Science n Engineering: Electrical, Photovoltaic,Telecom n Double Degree: Science/Engineering n 6 UOC n Waves n Physical
More informationHomework. Suggested exercises: 32.1, 32.3, 32.5, 32.7, 32.9, 32.11, 32.13, 32.15, 32.18, 32.20, 32.24, 32.28, 32.32, 32.33, 32.35, 32.37, 32.
Homework Reading: Chap. 32 and Chap. 33 Suggested exercises: 32.1, 32.3, 32.5, 32.7, 32.9, 32.11, 32.13, 32.15, 32.18, 32.20, 32.24, 32.28, 32.32, 32.33, 32.35, 32.37, 32.39 Problems: 32.46, 32.48, 32.52,
More informationCh 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 informationDr. 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 informationHandout 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 informationChapter 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 informationChapter 20 Lecture Notes
Chapter 20 Lecture Notes Physics 2424 - Strauss Formulas: B = µ 0 I/2πr B = Nµ 0 I/(2R) B = µ 0 ni Σ B l = µ 0 I F = Bqv sinθ r = mv/bq m = (er 2 /2V) B 2 F = ILB sinθ τ = NIAB sinϕ F/L = I 2 I 1 µ 0 /2πd
More informationChapter 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 informationElectrics. Electromagnetism
Electrics Electromagnetism Electromagnetism Magnetism is associated with charges in motion (currents): microscopic currents in the atoms of magnetic materials. macroscopic currents in the windings of an
More informationMagnetostatics 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 informationPhysics 202, Lecture 12. Today s Topics
Physics 202, Lecture 12 Today s Topics Magnetic orces (Ch. 27) Review: magnetic force, magnetic dipoles Motion of charge in uniform field: Applications: cyclotron, velocity selector, Hall effect Sources
More informationEvery magnet has a north pole and south pole.
Magnets - Intro The lodestone is a naturally occurring mineral called magnetite. It was found to attract certain pieces of metal. o one knew why. ome early Greek philosophers thought the lodestone had
More informationCh 30 - Sources of Magnetic Field
Ch 30 - Sources of Magnetic Field Currents produce Magnetism? 1820, Hans Christian Oersted: moving charges produce a magnetic field. The direction of the field is determined using a RHR. Oersted (1820)
More informationMagnetism. Magnets Source of magnetism. Magnetic field. Magnetic force
Magnetism Magnets Source of magnetism Magnetic field Magnetic force Magnets and magnetic force Historical First magnets were pieces of iron-bearing rock called loadstone (magnetite, Fe 3 O 4 ) found originally
More informationLECTURE 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 informationMagnetic Forces and Magnetic Fields
Magnetic Forces and Magnetic Fields 21.1 Magnetic Fields The behavior of magnetic poles is similar to that of like and unlike electric charges. 21.1 Magnetic Fields The needle of a compass is permanent
More informationMOVING CHARGES AND MAGNETISM
4 MOVING CHARGES AND MAGNETISM Moving charges can produce magnetic field. Magnetic field is produced around current carrying conductors also. The SI unit of magnetic induction (magnetic field intensity
More informationSources 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 informationGeneral Physics (PHYS )
General Physics (PHYS ) Chapter 22 Magnetism Magnetic Force Exerted on a current Magnetic Torque Electric Currents, magnetic Fields, and Ampere s Law Current Loops and Solenoids Magnetism in Matter GOT
More informationDisplacement 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 informationMagnetostatics. P.Ravindran, PHY041: Electricity & Magnetism 22 January 2013: Magntostatics
Magnetostatics Magnetic Fields We saw last lecture that some substances, particularly iron, possess a property we call magnetism that exerts forces on other magnetic materials We also saw that t single
More informationLecture #4.4 Magnetic Field
Lecture #4.4 Magnetic Field During last several lectures we have been discussing electromagnetic phenomena. However, we only considered examples of electric forces and fields. We first talked about electrostatics
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.
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 informationMarch 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 informationMagnets & Magnetic Fields
Magnets & Magnetic Fields Magnets Magnets have 2 poles, North and South if broken in half, each half will have both poles at the ends. Like poles repel, unlike poles attract. Hard Magnets- materials that
More informationAnnouncements. 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 informationChapter 17: Magnetism
Chapter 17: Magnetism Section 17.1: The Magnetic Interaction Things You Already Know Magnets can attract or repel Magnets stick to some things, but not all things Magnets are dipoles: north and south Labels
More informationChapter 27 Magnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces Lecture by Dr. Hebin Li Goals for Chapter 27 To study magnets and the forces they exert on each other To calculate the force that a magnetic field exerts on
More informationPHYS ND semester Dr. Nadyah Alanazi. Lecture 16
1 PHYS 104 2 ND semester 1439-1440 Dr. Nadyah Alanazi Lecture 16 2 Chapter 29 Magnetic Field 29.1 Magnetic Fields and Forces 29.2 Magnetic Force Acting on a Current-Carrying Conductor 29.4 Motion of a
More informationPhysics 212 Question Bank III 2006
A negative charge moves south through a magnetic field directed north. The particle will be deflected (A) North. () Up. (C) Down. (D) East. (E) not at all. The magnetic force on a moving charge is (A)
More informationModule 3: Electromagnetism
Module 3: Electromagnetism Lecture - 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 electromagnetic
More informationMagnetic 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 information1. Write the relation for the force acting on a charge carrier q moving with velocity through a magnetic field in vector notation. Using this relation, deduce the conditions under which this force will
More informationPhysics 212 Question Bank III 2010
A negative charge moves south through a magnetic field directed north. The particle will be deflected (A) North. () Up. (C) Down. (D) East. (E) not at all.. A positive charge moves West through a magnetic
More informationChapter 4: Magnetic Field
Chapter 4: Magnetic Field 4.1 Magnetic Field 4.1.1 Define magnetic field Magnetic field is defined as the region around a magnet where a magnetic force can be experienced. Magnetic field has two poles,
More informationGeneral Physics (PHY 2140)
General Physics (PHY 2140) Lecture 8 Electricity and Magnetism 1. Magnetism Application of magnetic forces Ampere s law 2. Induced voltages and induction Magnetic flux http://www.physics.wayne.edu/~alan/2140website/main.htm
More informationELECTROMAGNETISM The study of the relationship between electricity and magnetism is called
ELECTROMAGNETISM The study of the relationship between electricity and magnetism is called Electromagnetism Before, 1819 it was believed that there was no connection between electricity and magnetism.
More informationChapter 30. Sources of the Magnetic Field
Chapter 30 Sources of the Magnetic Field CHAPTER OUTLNE 30.1 The Biot Savart Law 30.2 The Magnetic Force Between Two Parallel Conductors 30.3 Ampère s Law 30.4 The Magnetic Field of a Solenoid 30.5 Magnetic
More informationMagnetism is associated with charges in motion (currents):
Electrics Electromagnetism Electromagnetism Magnetism is associated with charges in motion (currents): microscopic currents in the atoms of magnetic materials. macroscopic currents in the windings of an
More informationAgenda for Today. Elements of Physics II. Forces on currents
Forces on currents Physics 132: Lecture e 20 Elements of Physics II Agenda for Today Currents are moving charges Torque on current loop Torque on rotated loop Currents create B-fields Adding magnetic fields
More information1-1 Magnetism. q ν B.(1) = q ( ) (2)
1-1 Magnetism Magnets exert forces on each other just like charges. You can draw magnetic field lines just like you drew electric field lines. Magnetic north and south pole s behavior is not unlike electric
More informationMagnetic Fields Part 2: Sources of Magnetic Fields
Magnetic Fields Part 2: Sources of Magnetic Fields Last modified: 08/01/2018 Contents Links What Causes a Magnetic Field? Moving Charges Right Hand Grip Rule Permanent Magnets Biot-Savart Law Magnetic
More informationLecture 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 informationPHY132 Lecture 13 02/24/2010. Lecture 13 1
Classical Physics II PHY132 Lecture 13 Magnetism II: Magnetic torque Lecture 13 1 Magnetic Force MAGNETISM is yet another force that has been known since a very long time. Its name stems from the mineral
More informationMODULE 6 ELECTROMAGNETISM MAGNETIC FIELDS MAGNETIC FLUX VISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE MODULE 6 ELECTROMAGNETISM MAGNETIC FIELDS MAGNETIC FLUX Magnetic field (-field ): a region of influence where magnetic materials and electric currents are subjected to a magnetic
More informationChapter 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 informationMagnets. Magnetic vs. Electric
Magnets A force is applied to the iron filings causing them to align themselves to the direction of the magnetic field. A compass needle will tell you the direction of the field. Show Fields of little
More informationIt is the force experienced by a charged particle moving in a space where both electric and magnetic fields exist. F =qe + q(v B )
Moving Charges and Magnetism Moving Charges Moving charges produce magnetic field around them. SI unit of magnetic field is Tesla (T). Lorentz Force It is the force experienced by a charged particle moving
More informationLecture 27: MON 26 OCT Magnetic Fields Due to Currents II
Physics 212 Jonathan Dowling Lecture 27: MON 26 OCT Magnetic Fields Due to Currents II Jean-Baptiste Biot (1774-1862) Felix Savart (1791 1841) Electric Current: A Source of Magnetic Field Observation:
More information