PHY 184AnnouncementsReviewReview (2)Example: Cathode Ray TubeCathode Ray Tube (2)Particle Orbits in a Uniform BParticle Orbits in Uniform B (2)Example - Moving ElectronsClicker QuestionSlide 11Example: Mass Spectrometer (1)Example: Mass Spectrometer (2)Example: The Time Projection ChamberExample: The Time Projection Chamber (2)Example: The Time Projection Chamber (3)Events in the TPCExample - Momentum of a TrackOrbits in a Constant Magnetic FieldCyclotronsExample: Deuteron in CyclotronSpecial ClickerK500 Superconducting Cyclotron2/xx/07 184 Lecture 22 1PHY 184PHY 184PHY 184PHY 184Week 6 Spring 2007Lecture 22Title: The Lorentz Force = q v x B2/xx/07 184 Lecture 22 2AnnouncementsAnnouncementsAnnouncementsAnnouncementsHomework Set 5 is due next Tuesday at 8:00 am.The correction set to Midterm 1 is due next Tuesday at 6:00pm.2/xx/07 184 Lecture 22 3ReviewReviewReviewReviewThe force that a magnetic field exerts on a charge moving with velocity v is given byThe direction is sideways (RH rule).The magnitude of the forceIf the charge moves perpendicular to the magnetic field thenFBqvBsinFBqvBsinF qvBF qvBBvqFBBvqFB2/xx/07 184 Lecture 22 4Review (2)Review (2)Review (2)Review (2)The unit of magnetic field strength the tesla (T)Another unit of magnetic field strength that is often used but is not an SI unit is the gauss (G)Typically the Earth’s magnetic field is about 0.5 G at the surface.1 T = 1 NsCm1NAm1 G = 10-4 T10 kG = 1 T2/xx/07 184 Lecture 22 5Example: Cathode Ray TubeExample: Cathode Ray TubeExample: Cathode Ray TubeExample: Cathode Ray TubeConsider the cathode-ray tube used for lecture demonstrations.In this tube electrons form an electron beam when accelerated horizontally by a voltage of 136 V in an electron gun.The mass of an electron is 9.109410-31 kg while the elementary charge is 1.602210-19 C.(a) Calculate the velocity of the electrons in the beam after leaving the electron gun.m/s 1092.6 implies 6221veVmvqVUK2/xx/07 184 Lecture 22 6Cathode Ray Tube (2)Cathode Ray Tube (2)Cathode Ray Tube (2)Cathode Ray Tube (2)(b) If the tube is placed in a uniform magnetic field, in what direction is the electron beam deflected?(c) Calculate the magnitude of acceleration of an electron if the field strength is 3.65×10-4T.F ma qvBa qvBm1.6022 10 19 C 6.92 106 m/s 3.65 10 4 T 9.1094 10 31 kg4.44 1014 m/s2downward2/xx/07 184 Lecture 22 7Particle Orbits in a Uniform Particle Orbits in a Uniform BBParticle Orbits in a Uniform Particle Orbits in a Uniform BBTie a string to a rock and twirl it at constant speed in a circle over your head.The tension of the string provides the centripetal force that keeps the rock moving in a circle.The tension on the string always points to the center of the circle and creates a centripetal acceleration.A particle with charge q and mass m moves with velocity v perpendicular to a uniform magnetic field B.The particle will move in a circle with a constant speed v and the magnetic force F = qvB will keep the particle moving in a circle.2/xx/07 184 Lecture 22 8Particle Orbits in Uniform Particle Orbits in Uniform BB (2) (2)Particle Orbits in Uniform Particle Orbits in Uniform BB (2) (2)Recall centripetal accelerationNewton;’s second lawSo, for charged particle q in circular motion in magnetic field BBvqrvm 2a = v2/rF = m a2/xx/07 184 Lecture 22 9Example - Moving ElectronsExample - Moving ElectronsExample - Moving ElectronsExample - Moving ElectronsIn this photo, an electron beam is initially accelerated by an electric field.Then the electrons move in a circle perpendicular to the constant magnetic field created by a pair of Helmholtz coils.vFIs the magnetic field into the page or out of the page?(Remember that the magnetic force on an electron is opposite that on a proton.)The magnetic field is out of the page.2/xx/07 184 Lecture 22 10Clicker QuestionClicker QuestionClicker QuestionClicker QuestionThe figure shows the circular paths of two particles that travel at the same speed in a uniform magnetic field (directed into the page). One particle is a proton and the other is an electron. Which particle follows the smaller circle? A) the electron B) the proton C) Both, proton and electron travel along on the same circle2/xx/07 184 Lecture 22 11Clicker QuestionClicker QuestionClicker QuestionClicker QuestionThe figure shows the circular paths of two particles that travel at the same speed in a uniform magnetic field (directed into the page). One particle is a proton and the other is an electron. Which particle follows the smaller circle? A) the electron r mvqBr mvqB… for same speeds, r is proportional to m2/xx/07 184 Lecture 22 12Example: Mass Spectrometer (1)Example: Mass Spectrometer (1)Example: Mass Spectrometer (1)Example: Mass Spectrometer (1)Suppose that B=80mT, V=1000V. A charged ion (1.6022 10-19C) enters the chamber and strikes the detector at a distance x=1.6254m. What is the mass of the ion?Key Idea: The uniform magnetic field forces the ion on a circular path and the ion’s mass can be related to the radius of the circular trajectory.2/xx/07 184 Lecture 22 13Example: Mass Spectrometer (2)Example: Mass Spectrometer (2)Example: Mass Spectrometer (2)Example: Mass Spectrometer (2)Suppose that B=80mT, V=1000V. A charged ion (1.6022 10-19C) enters the chamber and strikes the detector at a distance x=1.6254m. What is the mass of the ion?From the figure: r=0.5xAlso need the velocity v after the ion is accelerated by the potential difference VeVmv 221evBrmv2Now solve for m3.4x10-25 kg2/xx/07 184 Lecture 22 14Example: The Time Projection Example: The Time Projection ChamberChamberExample: The Time Projection Example: The Time Projection ChamberChamberIn high-energy nuclear physics, new forms of matter are studied by colliding gold nuclei at very high energiesIn particle physics, new elementary particles are created and studied by colliding protons and anti-protons at the highest energiesIn these collisions, many particles are created that stream away from the interaction point at high speedsA simple particle detector is not sufficient to measure and identify these particlesA device that can help physicists study these collisions is the time projection chamber (TPC)2/xx/07
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