PHY2049: Chapter 281Chapter 28: Magnetic FieldsPHY2049: Chapter 282Magnetic Fields ÎMagnetic field (units, field lines) Magnetic field of the earth and other astronomical objectsÎEffects of magnetic fields on charges and currents Force on a moving charge Force on a current Torque on a current loop Path followed by particle in magnetic fieldÎGenerating magnetic fields Long wire Current loop SolenoidÎInstruments Mass spectrometers Cyclotrons and synchrotronsPHY2049: Chapter 283Reading QuizÎThe magnetic force on a moving charged particle is: (1) Perpendicular to the velocity (2) Parallel to the velocity (3) Parallel to the B field (4) Independent of the velocity (5) None of the abovePHY2049: Chapter 284Reading QuizÎ Consider +q moving relative to a B field as shown Force is parallel to v Force is parallel to B Force is into the page Force is out of the pageB+qPHY2049: Chapter 285Reading QuizÎWhen I cut a magnet into two pieces I get: An isolated north and south magnetic pole Two smaller magnets The two pieces are no longer magnetsPHY2049: Chapter 286Bar MagnetsÎTwo poles: “north” and “south”ÎLike poles repelÎUnlike poles attractÎMagnetic poles cannot be isolated NSSimilar to dipole field from electrostaticsPHY2049: Chapter 287Magnetic Monopoles?ÎCan any isolated magnetic charge exist? We would call this a “magnetic monopole” It would have a + or – magnetic chargeÎHow can we isolate this magnetic charge? Cut a bar magnet in half? NO!No one has ever found magnetic monopoles in natureWhat you getis a bunch oflittle magnets!PHY2049: Chapter 288Searches for Magnetic MonopolesPHY2049: Chapter 289Earth is a big magnet!!The North pole of a small magnet (compass) points towards geographic North because Earth’s magnetic South pole is up there!!Particles moving along field lines cause Aurora Borealis.http://science.nasa.gov/spaceweather/aurora/gallery_01oct03.htmlPHY2049: Chapter 2810What Causes Magnetism?ÎWhat is the origin of magnetic fields? Electric charge in motion! For example, a current in a wire loop produces a field very similar to that of a bar magnet (as we shall see). ÎUnderstanding the source of bar magnet field lies in understanding currents at the atomic level within matterOrbits of electrons about nucleiIntrinsic “spin” of electrons (more important effect)PHY2049: Chapter 2811Magnetic Field UnitsÎFrom the expression for force on a current-carrying wire: B = Fmax/ I L Units: Newtons/A⋅m ≡ Tesla (SI unit) Another unit: gauss = 10-4TeslaÎSome sample magnetic field strengths: Earth: B = 0.5 gauss = 0.5 x 10-4 T Galaxy: B ∼ 10-6gauss = 10-10T Bar magnet: B ∼ 100 – 200 gauss Strong electromagnet: B = 2 T Superconducting magnet: B = 5 – 10 T Pulse magnet: B ∼ 100 T Neutron star: B ∼ 108–109T Magnetar: B ∼ 1011TPHY2049: Chapter 2812PulsarsRapidly Rotating Neutron StarsEnormousMagnetic FieldsBeam off Beam onCrab PulsarR = 10 kmM = 1.4 solar massB ≈ 108TPeriod = 1/30 secPHY2049: Chapter 2813Magnetic Field BÎMagnetic field defined by magnetic force on a test chargeÎForce magnitude depends on direction of v relative to B v is parallel to B ⇒ sinφ = 0 v is perpendicular to B ⇒ sinφ = 1 v is at angle 45° to B ⇒ sinφ = 0.71ÎForce direction is perpendicular to both B andv Right hand rule (next slide)sinFqvBFqvBφ=×=GGGFqvB=0F=sin45FqvB=B+qvF (into page)PHY2049: Chapter 2814Right Hand RuleÎFirst point fingers in direction of velocity Curl fingers toward B field ⇒ Thumb points toward forceFvBPHY2049: Chapter 2815ExampleÎParticle with m = 1.5 g, q = −2μC moves with velocity 2,000 m/s through a magnetic field of 2.5 T at an angle of 30° to the field. Magnitude of force Direction of force: up out of the page, from RHR()()()()6sin 2 10 2.5 2000 0.5 0.005NFqBvφ−==× =B−qvF (up)PHY2049: Chapter 2816A charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here?1. Yes2. NoA B field can exist since if v || Bthere is no magnetic forceBqvPHY2049: Chapter 2817ÎA negative particle enters a magnetic field region. What path will it follow? (1) A (2) B (3) C (4) D (5) Ex x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xMagnetic Force ABCDE(1)RHR says it bends down (− charge)(2)But force cannot instantaneously change v(3)So the answer is D, not EPHY2049: Chapter 2818Magnetic Force on Current-Carrying WireÎMagnitude of force Easy to derive from charge, number density & drift velocity of individual charge carriers ÎDirection of force: RHRsinFiBLφ=PHY2049: Chapter 2819ExampleÎA 4 m long wire carries current of 500A in NE direction Magnitude of force (B = 0.5 gauss = 5 × 10-5T, pointing N) Direction of force: Upwards, from RHRÎCan adjust current in wire to balance against gravity Calculate mass from density, length and cross-sectional area Good exam problem!siniBL mgφ=()()()()5sin 500 5 10 4 0.71 0.071NFiBLφ−==× =mLAρ=PHY2049: Chapter 2820Magnetic Force ÎA vertical wire carries a current 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 IBI is parallel to B, sono magnetic forcePHY2049: Chapter 2821Magnetic Field and WorkÎMagnetic force is alwaysperpendicular to velocity Therefore B field does no work! Why? BecauseÎConsequences Kinetic energy does not change Speed does not change Only direction changes Particle moves in a circle (if )()0KFxFvtΔ=⋅Δ=⋅Δ=GGGGvB⊥GGPHY2049: Chapter 2822x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x xTrajectory in a Constant Magnetic FieldÎA charge q enters B field with velocity v perpendicular to B. What path will q follow? Force is always ⊥ velocity and ⊥ B Path will be a circle. F is the centripetal force needed to keep the charge in its circular orbit. Let’s calculate radius RFFvRvBqFvPHY2049: Chapter 2823x x x x x x x x x x x x x x x x xx x x x x x x x x x
View Full Document