* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Introduction to Magnetism - Level 5 Physics
History of physics wikipedia , lookup
Standard Model wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Yang–Mills theory wikipedia , lookup
History of subatomic physics wikipedia , lookup
Electric charge wikipedia , lookup
Anti-gravity wikipedia , lookup
Renormalization wikipedia , lookup
Maxwell's equations wikipedia , lookup
Time in physics wikipedia , lookup
History of quantum field theory wikipedia , lookup
Neutron magnetic moment wikipedia , lookup
Speed of gravity wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Magnetic field wikipedia , lookup
Electrostatics wikipedia , lookup
Condensed matter physics wikipedia , lookup
Field (physics) wikipedia , lookup
Work (physics) wikipedia , lookup
Fundamental interaction wikipedia , lookup
Superconductivity wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Magnetic monopole wikipedia , lookup
Electromagnet wikipedia , lookup
Introduction to Magnetism Introduction to Magnetism Level 5 Physics January 2013 Material adapted from MIT 8.02 course notes Introduction to Magnetism Introduction Everyday Knowledge What is Magnetism? What do you already know about magnetism? Introduction to Magnetism Introduction Everyday Knowledge What is Magnetism? What do you already know about magnetism? Perhaps you have played with a magnet before and know that it has a north pole and a south pole. Unlike poles attract while like poles repel. Introduction to Magnetism Introduction Everyday Knowledge Observing “Action at a Distance” Perhaps you have also noticed that magnets seem to produce a force that “acts over distance”. Introduction to Magnetism Introduction Everyday Knowledge Observing “Action at a Distance” Perhaps you have also noticed that magnets seem to produce a force that “acts over distance”. This may seem similar to areas in physics you have already studied: Introduction to Magnetism Introduction Everyday Knowledge Observing “Action at a Distance” Perhaps you have also noticed that magnets seem to produce a force that “acts over distance”. This may seem similar to areas in physics you have already studied: GMm Gravitational force: F~g = − 2 r̂ r where G = 6.67x10−11 N · m2 /kg 2 ke Qq Electric force: F~e = r̂ r2 9 2 where ke = 9.0x10 N · m /C 2 Introduction to Magnetism Introduction Everyday Knowledge Observing “Action at a Distance” Perhaps you have also noticed that magnets seem to produce a force that “acts over distance”. This may seem similar to areas in physics you have already studied: GMm Gravitational force: F~g = − 2 r̂ r where G = 6.67x10−11 N · m2 /kg 2 ke Qq Electric force: F~e = r̂ r2 9 2 where ke = 9.0x10 N · m /C 2 Therefore, we might suspect that there exists a magnetic force. Introduction to Magnetism Introduction Field Theory Revising “Action at a Distance” The idea behind “action at a distance” is an old theory that a force between two objects can be transmitted through empty space. Introduction to Magnetism Introduction Field Theory Revising “Action at a Distance” The idea behind “action at a distance” is an old theory that a force between two objects can be transmitted through empty space. What actually happens is the force is transmitted through stresses in the intervening spaces until the second object is reached. Introduction to Magnetism Introduction Field Theory Fields This is the basis of modern field theory, which was proposed by Maxwell in 1873. Fields allow us to specify the effect a source will have on a second agent at any position in space. Introduction to Magnetism Introduction Field Theory Fields This is the basis of modern field theory, which was proposed by Maxwell in 1873. Fields allow us to specify the effect a source will have on a second agent at any position in space. Recall the following fields you have already seen: Introduction to Magnetism Introduction Field Theory Fields This is the basis of modern field theory, which was proposed by Maxwell in 1873. Fields allow us to specify the effect a source will have on a second agent at any position in space. Recall the following fields you have already seen: F~g GM Gravitational field: ~g = = − 2 r̂ m r ~ Fe ke Q Electrical field: ~E = = 2 r̂ q r Introduction to Magnetism Introduction Field Theory Fields This is the basis of modern field theory, which was proposed by Maxwell in 1873. Fields allow us to specify the effect a source will have on a second agent at any position in space. Recall the following fields you have already seen: F~g GM Gravitational field: ~g = = − 2 r̂ m r ~e F k Q e Electrical field: ~E = = 2 r̂ q r Introduction to Magnetism Introduction Field Theory Fields This is the basis of modern field theory, which was proposed by Maxwell in 1873. Fields allow us to specify the effect a source will have on a second agent at any position in space. Recall the following fields you have already seen: F~g GM Gravitational field: ~g = = − 2 r̂ m r ~e F k Q e Electrical field: ~E = = 2 r̂ q r Therefore, we might suspect that there exists a magnetic field. Introduction to Magnetism Introduction Plan Topics The magnetic forces caused by magnetic fields that we have inferred do indeed exist. Introduction to Magnetism Introduction Plan Topics The magnetic forces caused by magnetic fields that we have inferred do indeed exist. Topics we will address: Introduction to Magnetism Introduction Plan Topics The magnetic forces caused by magnetic fields that we have inferred do indeed exist. Topics we will address: Formula for magnetic force Sources of magnetic fields Magnetic materials and applications Introduction to Magnetism Theory Point Charge Experimental Observations Experimenters have made the following observations about a ~ particle of charge q moving at a velocity ~v in a magnetic field B: Introduction to Magnetism Theory Point Charge Experimental Observations Experimenters have made the following observations about a ~ particle of charge q moving at a velocity ~v in a magnetic field B: 1 The magnitude of F~B exerted on the charged particle is proportional to both v and q Introduction to Magnetism Theory Point Charge Experimental Observations Experimenters have made the following observations about a ~ particle of charge q moving at a velocity ~v in a magnetic field B: 1 The magnitude of F~B exerted on the charged particle is proportional to both v and q 2 ~ The magnitude and direction of F~B depends on ~v and B Introduction to Magnetism Theory Point Charge Experimental Observations Experimenters have made the following observations about a ~ particle of charge q moving at a velocity ~v in a magnetic field B: 1 The magnitude of F~B exerted on the charged particle is proportional to both v and q 2 3 ~ The magnitude and direction of F~B depends on ~v and B ~ the magnetic force F~B has When ~v makes an angle θ with B, ~ and magnitude direction perpendicular to both ~v and B proportional to sin θ Introduction to Magnetism Theory Point Charge Experimental Observations Experimenters have made the following observations about a ~ particle of charge q moving at a velocity ~v in a magnetic field B: 1 The magnitude of F~B exerted on the charged particle is proportional to both v and q 2 3 4 ~ The magnitude and direction of F~B depends on ~v and B ~ the magnetic force F~B has When ~v makes an angle θ with B, ~ and magnitude direction perpendicular to both ~v and B proportional to sin θ When the sign of q switches, the direction of F~B also switches. Introduction to Magnetism Theory Point Charge Experimental Observations Experimenters have made the following observations about a ~ particle of charge q moving at a velocity ~v in a magnetic field B: 1 The magnitude of F~B exerted on the charged particle is proportional to both v and q 2 3 4 ~ The magnitude and direction of F~B depends on ~v and B ~ the magnetic force F~B has When ~v makes an angle θ with B, ~ and magnitude direction perpendicular to both ~v and B proportional to sin θ When the sign of q switches, the direction of F~B also switches. What formula for F~B satisfies these criteria? Introduction to Magnetism Theory Point Charge Review of Special Products Dot Product ~ and B ~ separated by angle θ The dot product of two vectors A produces a scalar: ~ ·B ~ = kAk kBk cos θ A Introduction to Magnetism Theory Point Charge Review of Special Products Dot Product ~ and B ~ separated by angle θ The dot product of two vectors A produces a scalar: ~ ·B ~ = kAk kBk cos θ A Cross Product ~ and B ~ separated by angle θ The cross product of two vectors A produces a vector: ~ ~ A × B = kAk kBk sin θ with direction given by the right-hand rule Introduction to Magnetism Theory Point Charge Magnetic Force on Point Charge Magnetic Force The magnetic force on a particle of charge q moving at a velocity ~ is given by the formula ~v in a magnetic field B ~ F~B = q~v × B Introduction to Magnetism Theory Current-Carrying Wire Current Electric current is simply a collection of moving charged particles. Thus, a wire carrying an electric current I should experience a magnetic force as well. Introduction to Magnetism Theory Current-Carrying Wire Current Electric current is simply a collection of moving charged particles. Thus, a wire carrying an electric current I should experience a magnetic force as well. Suppose you have a wire of length ` and cross-sectional area A. If each charged particle has charge q and n is the number of charges per unit volume, the total charge of the wire is Qtotal = q(nA`) Introduction to Magnetism Theory Current-Carrying Wire Current Electric current is simply a collection of moving charged particles. Thus, a wire carrying an electric current I should experience a magnetic force as well. Suppose you have a wire of length ` and cross-sectional area A. If each charged particle has charge q and n is the number of charges per unit volume, the total charge of the wire is Qtotal = q(nA`) If the charged particles move at an average drift velocity of v~d , the current is I = nqvd A Introduction to Magnetism Theory Current-Carrying Wire Derivation We can derive the magnetic force on a wire using Qtotal = q(nA`) and I = nqvd A. Introduction to Magnetism Theory Current-Carrying Wire Derivation We can derive the magnetic force on a wire using Qtotal = q(nA`) and I = nqvd A. ~ F~B = Qtotal v~d × B ~ = qnA`(v~d × B) ~ = nqvd A(~` × B) ~ = I (~` × B) where ~` is a length vector with magnitude ` and the same direction as the current (and v~d ) Introduction to Magnetism Theory Current-Carrying Wire Magnetic Force on Current-Carrying Wire Magnetic Force The magnetic force on a wire carrying current I with length vector ~` in a magnetic field B ~ is given by the formula ~ F~B = I ~` × B Introduction to Magnetism Theory Current-Carrying Wire Closed Loop ~ is The differential corresponding to F~B = I ~` × B ~ d F~B = I (d~s × B) where d~s is a small segment of the wire. Introduction to Magnetism Theory Current-Carrying Wire Closed Loop ~ is The differential corresponding to F~B = I ~` × B ~ d F~B = I (d~s × B) where d~s is a small segment of the wire. If the wire forms a closed loop and the magnetic field is constant, then the total force on the wire is zero. H ~ = ~0 F~B = I ( d~s) × B Introduction to Magnetism Theory Units Tesla ~ is the tesla (T). Its equivalence The SI unit for a magnetic field B ~ ~ can be derived from FB = q~v × B. Newton (Coulomb)(meter/second) N =1 C · m/s N =1 A·m 1 tesla = 1T = 1 Introduction to Magnetism Theory Units Tesla ~ is the tesla (T). Its equivalence The SI unit for a magnetic field B ~ ~ can be derived from FB = q~v × B. Newton (Coulomb)(meter/second) N =1 C · m/s N =1 A·m 1 tesla = 1T = 1 Another common non-SI unit is the gauss (G), where 1T = 104 G . Introduction to Magnetism Theory Units Tesla ~ is the tesla (T). Its equivalence The SI unit for a magnetic field B ~ ~ can be derived from FB = q~v × B. Newton (Coulomb)(meter/second) N =1 C · m/s N =1 A·m 1 tesla = 1T = 1 Another common non-SI unit is the gauss (G), where 1T = 104 G . For reference, the magnetic field strength at the Earth’s surface varies from 0.25 to 0.65 gauss. Introduction to Magnetism Questions Concept Questions Point Charge Force Consider a particle of charge q with velocity vector ~v moving in a ~ What is the magnetic force F~B if ~v is parallel to magnetic field B. ~ B? ~ 1 −q~ v×B 2 ~0 3 ~ q~v × B Introduction to Magnetism Questions Concept Questions Point Charge Force Consider a particle of charge q with velocity vector ~v moving in a ~ What is the magnetic force F~B if ~v is parallel to magnetic field B. ~ B? ~ 1 −q~ v×B 2 ~0 3 ~ q~v × B Correct Answer: 2 ~ is 0, and since the cross product (The angle between ~v and B involves sin(0), the magnetic force is ~0.) Introduction to Magnetism Questions Concept Questions Point Charge Velocity Consider a particle of charge q with velocity vector ~v moving in a ~ How does ~v change due to F~B if ~v is not parallel magnetic field B. ~ to B? 1 No change 2 Only magnitude changes 3 Only direction changes 4 Magnitude and direction change Introduction to Magnetism Questions Concept Questions Point Charge Velocity Consider a particle of charge q with velocity vector ~v moving in a ~ How does ~v change due to F~B if ~v is not parallel magnetic field B. ~ to B? 1 No change 2 Only magnitude changes 3 Only direction changes 4 Magnitude and direction change Correct Answer: 3 (F~B is perpendicular to ~v, so it can only modify the direction.) Introduction to Magnetism Questions Concept Questions Negative Point Charge Consider a negative particle with velocity vector ~v moving in a ~ as shown below. What is the direction of the magnetic field B resulting magnetic force? 1 Out of the page 2 In the plane of the page 3 Into the page Introduction to Magnetism Questions Concept Questions Negative Point Charge Consider a negative particle with velocity vector ~v moving in a ~ as shown below. What is the direction of the magnetic field B resulting magnetic force? 1 Out of the page 2 In the plane of the page 3 Into the page Correct Answer: 1 (The right-hand rule produces the correct magnetic force for a positive charge. Reverse the direction given by the right-hand rule for a negative charge.) Introduction to Magnetism Questions Concept Questions Point Charge Work In the same situation as the previous problem, F~B will do what amount of work on the particle over time? 1 Negative 2 Zero 3 Postive Introduction to Magnetism Questions Concept Questions Point Charge Work In the same situation as the previous problem, F~B will do what amount of work on the particle over time? 1 Negative 2 Zero 3 Postive Correct Answer: 2 ~ · ~vdt = 0.) (dW = F~B · d~s = q(~v × B) Introduction to Magnetism Questions Concept Questions Force on Wire Suppose a positive current is traveling downward through a wire. A portion of the wire runs through a uniform magnetic field pointing out of the page. Which behavior of the wire would you expect to see? 1 2 3 Introduction to Magnetism Questions Concept Questions Force on Wire Suppose a positive current is traveling downward through a wire. A portion of the wire runs through a uniform magnetic field pointing out of the page. Which behavior of the wire would you expect to see? 1 2 Correct Answer: 2 (Apply the right hand rule.) 3 Introduction to Magnetism Questions Concept Questions Closed Loop A semi-circular loop with radius R carrying a current I is placed in a uniform magnetic field. What is the net force on only the curved portion of the loop? 1 2RIB, into the page 2 0 3 2RIB, out of the page Introduction to Magnetism Questions Concept Questions Closed Loop A semi-circular loop with radius R carrying a current I is placed in a uniform magnetic field. What is the net force on only the curved portion of the loop? 1 2RIB, into the page 2 0 3 2RIB, out of the page Correct Answer: 1 (If the wire forms a closed loop and the magnetic field is constant, then the total force on the wire is zero.)