PHY PHY 184 184 Week 6 Spring 2007 Lecture 22 Title The Lorentz Force q v x B 2 xx 07 184 Lecture 22 1 Announcements Homework 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 2 Review The force that a magnetic field exerts on a charge moving with velocity v is given by F FBB qqvv B B The direction is sideways RH rule The magnitude of the force FB qvBsin If the charge moves perpendicular to the magnetic field then F qvB 2 xx 07 184 Lecture 22 3 Review 2 The unit of magnetic field strength the tesla T Ns N 1T 1 1 Cm Am Another unit of magnetic field strength that is often used but is not an SI unit is the gauss G 1 G 10 4 T 10 kG 1 T Typically the Earth s magnetic field is about 0 5 G at the surface 2 xx 07 184 Lecture 22 4 Example Cathode Ray Tube Consider 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 1094 10 31 kg while the elementary charge is 1 6022 10 19 C a Calculate the velocity of the electrons in the beam after leaving the electron gun K U qV 1 mv2 2 2 xx 07 eV implies 184 Lecture 22 v 6 92 106 m s 5 Cathode Ray Tube 2 b If the tube is placed in a uniform magnetic field in what direction is the electron beam deflected downward c Calculate the magnitude of acceleration of an electron if the field strength is 3 65 10 4T F ma qvB qvB 1 6022 10 a m 2 xx 07 19 C 6 92 10 6 m s 3 65 10 4 T 9 1094 10 31 kg 184 Lecture 22 4 44 10 14 m s 2 6 Particle Orbits in a Uniform B Tie 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 7 Particle Orbits in Uniform B 2 Recall centripetal accelerationa Newton s second law v2 r F ma So for charged particle q in circular motion in magnetic field B v2 m q v B r 2 xx 07 184 Lecture 22 8 Example Moving Electrons In 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 Is the magnetic field into the page F or out of the page Remember that the magnetic force on an electron is opposite that on a proton The magnetic field v is out of the page 2 xx 07 184 Lecture 22 9 Clicker Question The 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 circle 2 xx 07 184 Lecture 22 10 Clicker Question The 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 mv r qB for same speeds r is proportional to m 2 xx 07 184 Lecture 22 11 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 12 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 5x Also need the velocity v after the ion is accelerated by the potential difference V mv2 evB r 2 1 mv 2 eV Now solve for m 2 xx 07 184 Lecture 22 3 4x10 25 kg 13 Example The Time Projection Chamber In high energy nuclear physics new forms of matter are studied by colliding gold nuclei at very high energies In particle physics new elementary particles are created and studied by colliding protons and antiprotons at the highest energies In these collisions many particles are created that stream away from the interaction point at high speeds A simple particle detector is not sufficient to measure and identify these particles A device that can help physicists study these collisions is the time projection chamber TPC 2 xx 07 184 Lecture 22 14 Example The Time Projection Chamber 2 The STAR TPC consists of a large cylinder filled with a carefully chosen gas 90 argon 10 methane that allows free electrons to drift without recombining As created charged particles pass through the gas the particles ionize the atoms of the gas releasing free electrons An electric field is applied between the center of the TPC and the caps of the cylinder that exerts an electric force on these freed electrons making them drift to the end caps of the TPC where they are recorded electronically Using the drift time and the recording positions the computer software reconstructs the trajectories that the produced particles took through the TPC 2 xx 07 184 Lecture 22 15 Example The Time Projection Chamber 3 The TPC sits inside a giant solenoid magnet shown to the right with the magnetic field pointing along the beam direction The produced charged particles have a component of their velocity that is perpendicular to the magnetic field and thus have circular trajectories when viewed end on From the radius of curvature one can extract the particle momentum 2 xx 07 184 Lecture 22 16 Events in the TPC Here are two events in the STAR TPC at Brookhaven National Lab Magnetic field is directed into the screen Let s analyze this track 2 xx 07 184 Lecture 22 17 Example Momentum of a Track Calculate the momentum …
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