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Exam 1: Exam 1: *Covers all readings, lectures, homework from Chapters 17 through 19 *Exam 1: Tuesday September 28, 2010 from 8 PM - 10 PM *The exam will be multiple choice and is meant to be done within 75 minutes by a well-prepared student. We will give 120 minutes starting promptly at the listed time, so please be on time! * Room PHYS 112 for last names A through K * Room PHYS 114 for last names L through Z Be sure to bring your student ID card, calculator, pencil and your own one-page (two-side) crib sheet. NOTE THAT FEW EQUATIONS WILL BE GIVEN – YOU ARE REMINDED THAT IT IS YOUR RESPONSIBILITY TO CREATE WHATEVER TWO-SIDED CRIB SHEET YOU WANT TO BRING TO THIS EXAM. 9/21/10 1 Magnetic Field 9/21/10 2 Bar Magnets • Bar magnet ... two poles: N and S Like poles repel; Unlike poles attract. • Magnetic Field lines: (defined in same way as electric field lines, direction and density) S S N N N S S Attraction • Large Magnetic fields are used in MRI (Nobel prize for medicine in 2003) • Extremely Large magnetic field are found in some stars • Earth has a Magnetic Field 9/21/10 N S 3 9/21/10 N Repulsion From North to South 4 1 DEMO of Magnetic Field Lines Magnetic Monopoles • One explanation: there exists magnetic charge, just like electric charge. An entity which carried this magnetic charge would be called a magnetic monopole (having + or - magnetic charge). Electric Field Lines of an Electric Dipole • How can you isolate this magnetic charge? Try cutting a bar magnet in half: S Magnetic Field Lines of a bar magnet S 9/21/10 N S N S N • In fact no attempt yet has been successful in finding magnetic monopoles in nature but scientists are looking for them. N 5 Magnetic Force on a Moving Charge 9/21/10 6 Right Hand Rule Direction of FB is perpendicular to plane containing v & B. If q is positive, FB has the same sign as v x B. If q is negative, FB has the opposite sign of v x B. FB = qv × B F = q vB sin φ FB is never parallel to v. FB can only change the direction of the particle not the speed. 9/21/10 7 9/21/10 8 2 More on Magnetic Force The Magnetic Force F = qv × B • The magnetic force on a charged object that moves in a magnetic field does not do any work, because it’s perpendicular to v. • The magnetic force cannot change the magnitude of the velocity of a charged object, but can change the direction of motion. B = steering wheel, E = accelerator or brake pedal, so to speak • The SI unit for magnetic field is tesla (T): 1T =1 -4 ~Earth’s surface field! B B x x x x x x v x x x x x x +q FB N N N =1 =1 C⋅m / s C/s⋅m A⋅m A common unit gauss (G): 1 G = 10 T 9/21/10 B x x x x x x The direction of the force is: v v x +q +q FB (into the page) FB=0 (sin(0)=0) x x x x x x x x x x x x x x x x x x x x x x x x v B x x x x x x x x x x x x v F F q 9 9/21/10 10 Top view of Current-Carrying Bar Sliding on two current carrying frictionless rails in a magnetic field. I Magnetic Force on a Current-Carrying Wire V + – I F B THIS IS A FORM OF ELECTRIC MOTOR, TURNING ELECTRICAL INTO MECHANICAL ENERGY Note that this example assumes that the magnetic field caused by the currents in the rails is negligible compared to the external magnetic field B shown. I motion by reversing Direction of I, by reversing V The length L is the distance between the rails, where B is and where the current I flows in the green bar. 9/21/10 11 9/21/10 DEMO 12 3 Motion of a Point Charge in a Magnetic Field Trajectory in Constant Magnetic Field • Suppose charge q enters B field with velocity v as shown below. What will be the path q follows? B cannot change |v| of a charged particle. ⇒ B cannot change the kinetic energy of a charged particle. B can only change the direction of a particle. x x x x x x x x x x x x x x x x x x x x x x x x B v x x x x x x x x x x x x F q v F R 9/21/10 glow of ionized gas 13 Motion of a Point Charge in a Magnetic Field 9/21/10 14 Period of Circular Motion The period of the motion is or, the angular frequency 9/21/10 15 9/21/10 16 4 Mass Spectrometer (Ions with same KE) • Mass Spectrometer (Ions with same KE) Working with both equations : The purpose of a mass spectrometer is to separate ions by mass and measure the mass of each type of ion. • If positive ions start from rest and move through a potential difference, V, the ions’ kinetic energy when they enter the magnetic field equals their loss in potential energy: First solve for the velocity on the first one, v Then substitute it on the kinetic energy equation What kind of charge do the ions in the picture have? 9/21/10 17 9/21/10 A mass spectrometer can be improved if instead of having ions with the same kinetic energy entering the B field we have ions with the same velocity. 18 5