Understanding Magnetism: Earth's Fields and Magnetic Forces on Charges and Currents, Quizzes of Physics

Download Understanding Magnetism: Earth's Fields and Magnetic Forces on Charges and Currents and more Quizzes Physics in PDF only on Docsity! Chapter 19: Magnetic Fields a ~~ ° a . 7 we eo @ B \ f 8 © 8 8 Xe eo / + t etect eo fe © © © 4e ff 1 8 t | | | ——_——*: 4 = 8t¢ a Highest Lowest energy energy PHY 2054: Chapter 19 PHY2054: Chapter 19 2 Magnetic Fields Magnetic field (units, field lines) Magnetic field of the earth and other astronomical objects Effects 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 field Generating magnetic fields Long wire Current loop Solenoid Instruments Mass spectrometers Cyclotrons and synchrotrons PHY2054: Chapter 19 5 Reading Quiz Consider +q moving relative to a B field as shown. What is the direction of the magnetic force? Force is parallel to v Force is parallel to B Force is into the page Force is out of the page B +q PHY2054: Chapter 19 6 Reading Quiz Consider +q moving relative to a B field as shown. What is the direction of the magnetic force? Force is parallel to v Force is parallel to B Force is into the page Force is out of the page B +q Fig. 19-1, p.625 ‘© 2006 Brooks/Cole - Thomson PHY2054: Chapter 19 10 Magnetic Monopoles? Can any isolated magnetic charge exist? We would call this a “magnetic monopole” It would have a + or – magnetic charge How can we isolate this magnetic charge? Cut a bar magnet in half? NO! Magnetic monopoles have never been seen! What you get is a bunch of little magnets! Searches for Magnetic Monopoles 20 Sep 1998 hep-ph/9 809420 v Interactions of a Massive Slow Magnetic Monopole with Matter LV. Kolokolov, P.V. Vorob’ev Budker Institute of Nuclear Physics (BINP) Novosibirsk, Russia 630090. VOROBYOV@inp.nsk.su V.V. Ianovski Petersburg Nuclear Physics Institute (PNPT) Gatchina St. Petersburg Russia 188350. LANOVSK1@lnpi.spb.su Interactions of a massive magnetic monopole with matter are con- sidered. We discuss the possibility of creating the ferromagnetic _de- tector to search for cosmic magnetic monopoles. Introduction A concept of & magnetic monopole hes been introduced into modern physics in 1931 by Paul Dirac [1]. He postulated existence of an isolated magnetic charge g. Using general principles of quantum mechanics, he has related the electric and magnetic charge values: ge = fhe, where e is the electron electric charge, & is the Plank constant, ¢ is the speed of light, 2 = +1, 2... is an integer. Kumerous but unsuccessful attempts of experimental search for this magnetic monopole on accelerators and in cosmic rays [2, 3) have been done since then. Among them, exotic installations like the steel furnace have been proposed for accumulation of monopoles for subsequent detection [4]. Attempts of search for Dirac’s monopole by the ferromagnetic trap and the accelerators have been performed too [5]. PHY2054: Chapter 19 11 PHY2054: Chapter 19 12 Earth 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.html PHY2054: Chapter 19 15 Magnetic Field Units From the expression for force on a current-carrying wire: B = Fmax / I L Units: Newtons/A⋅m ≡ Tesla (SI unit) Another unit: 1 gauss = 10-4 Tesla Some sample magnetic field strengths: Earth: B = 0.5 gauss = 0.5 x 10-4 T Galaxy: B ∼ 10-6 gauss = 10-10 T 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 – 109 T Magnetar: B ∼ 1011 T PHY2054: Chapter 19 16 Pulsars Rapidly Rotating Neutron Stars Enormous Magnetic Fields Beam off Beam on Crab Pulsar R = 10 km M = 1.4 solar mass B ≈ 108 T Period = 1/30 sec PHY2054: Chapter 19 17 Magnetic Force on Moving Charge Magnetic force acts only on moving charge Force direction is perpendicular to both B and v Right hand rule (next slide) Force direction depends on sign of charge Force is in opposite direction from positive charge Force 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 = 0.71 sinF qvB φ= F qvB= 0F = sin 45F qvB= PHY2054: Chapter 19 20 Example Particle with m = 2.0 g, q = −2μC moves with v = 2,000 m/s through B field of 2.5 T at an angle of 30° to the field. Magnitude of force Direction of force: up out of the page. Use RHR and take opposite direction because of −q B −q v F is up out of page ( )( )( )( )6 2 sin 2 10 2000 2.5 0.5 0.005N / 0.005/ 0.002 2.5m/s F qvB a F m φ −= = × = = = = PHY2054: Chapter 19 21 Quiz A charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here? (1) Yes (2) No A B field can exist since if v || B there is no magnetic force PHY2054: Chapter 19 22 A negative particle enters a magnetic field region. What path will it follow? (1) A (2) B (3) C (4) D (5) E 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 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 x x x x Magnetic Force A B C D E (1) RHR says it bends down (− charge) (2) But force cannot instantaneously change v and the velocity vector bends continuously (3) So the answer is D, not E