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Transcript
PHYS 221 General Physics II Magnets, Magnetic Fields Spring 2015 Assigned Reading: 20.1 – 20.4 Lecture 9 Review: RC Circuit In the process of charging, the voltage on capacitor changes as: Vc (t) (1 e t / ) In the process of discharging, the voltage on capacitor changes as: Vc (t) e Phys 221 Spring 2014 t / Lecture 09 2 Ammeters • An ammeter is a device that measures current. • An ammeter must be connected in series with the desired circuit branch. • An ideal ammeter will measure current without changing its value. – Must have a very low resistance. Phys 221 Spring 2014 Lecture 09 3 Voltmeters • A voltmeter measures the voltage across a circuit element. • It must be connected in parallel with the element of interest. • An ideal voltmeter should measure the voltage. without changing its value. – The voltmeter should have a very high resistance. Phys 221 Spring 2014 Lecture 09 4 Magnetic Field • • • Phys 221 Spring 2014 Lecture 09 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 5 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) N S S N N N S S Attraction Repulsion From North to South outside From South to North inside Always close on themselves Phys 221 Spring 2014 Lecture 09 6 Magnetic Field • The magnetic poles are indicated at the ends of the bar magnet – Called north and south • The magnetic poles are analogous to positive and negative charges • The north poles of the filings are attracted to the south pole of the bar magnet • Magnetic field lines form closed loops. Phys 221 Spring 2014 Lecture 09 7 DEMO of Magnetic Field Lines Electric Field Lines of an Electric Dipole + - Magnetic Field Lines of a bar magnet Phys 221 Spring 2014 Lecture 09 8 i>Clicker question A Which drawing shows the correct field lines for a bar magnet? (A) (B) S N S N S N B (C) C Phys 221 Spring 2014 Lecture 09 9 Horseshoe Magnet • It can be made by bending a bar magnet. • There are poles at the ends of the horseshoe. • The field is largest in the horseshoe gap. • The field is directed across the gap. Phys 221 Spring 2014 Lecture 09 10 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). • How can you isolate this magnetic charge? Try cutting a bar magnet in half: S 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. Phys 221 Spring 2014 Lecture 09 11 Magnetic Force on a Moving Charge The force F on a charge q moving with velocity v through a region of space with a magnetic field B is given by: Phys 221 Spring 2014 Lecture 09 12 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 is never parallel to v. FB can only change the direction of the particle not the speed. Phys 221 Spring 2014 Lecture 09 13 More on Magnetic Force • 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 SI unit for magnetic field is tesla (T): -4 A common unit gauss (G): 1 G = 10 T Phys 221 Spring 2014 Lecture 09 ~Earth’s surface field! 14 The Magnetic Force F q v B The direction of the force is: B B x x x x x x x x x x x x v v v x x x x x x FB B +q 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 x x x x x x x x x x x x v Phys 221 Spring 2014 F F Lecture 09 B q 15 Motion in Uniform Magnetic Field 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. Phys 221 Spring 2014 Lecture 09 glow of ionized gas 16 i>Clicker question Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 2 1 v = 75 m/s q = +25 mC What is the direction of the magnetic field in region 2? A. up B. down C. left D. right E. into page F. out of page Phys 221 Spring 2014 Lecture 09 17 Trajectory in Constant Magnetic Field • Suppose charge q enters B field with velocity v as shown below. What will be the path q follows? 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 v F F q R Phys 221 Spring 2014 Lecture 09 18 Motion in Uniform Magnetic Field • Assume a charged particle moves perpendicular to the magnetic field. • The angle between the velocity and the field is 90°. • Therefore, the force is qvB. • The particle will move in a circle. • The circle lies in the plane perpendicular to the magnetic field lines. Phys 221 Spring 2014 Lecture 09 19 Motion of a Point Charge in a Magnetic Field FB qv B If v is B then FB qvB FB ma qvB Charge follows uniform circular motion thus there is a centripetal force on the charge mv 2 Fc r The only force acting on the charge is the magnetic mv 2 qvB r Phys 221 Spring 2014 mv r qB Lecture 09 20 Period of Circular Motion The period of the motion is 2r 2 mv 2m T v v qB qB Called the cyclotron period. or, the angular frequency 2 qB 2f T m only a function of q/m, but not the velocity v! Larger v: circumference grows IN PROPORTION Phys 221 Spring 2014 Lecture 09 21 Mass Spectrometer • Allows for the separation of ions according to their mass or charge. • The ions enter with some speed v. • They pass into a region where the magnetic field is perpendicular to the velocity. • The ions travel in a circle in the mass spectrometer. Phys 221 Spring 2014 Lecture 09 22 Mass Spectrometer • The radius of the circle is mv/qB. – Ions with different masses will travel in arcs with different radii. • Mass spectrometer can also be used to find the composition of a material. – Measure the values of v, B and r. – Calculate charge-to-mass ratio, q/m. Phys 221 Spring 2014 Lecture 09 23 Helical Motion • Assume a charged particle moves neither parallel nor perpendicular to the magnetic field. • The angle between the velocity and the field varies. • The path of the particle is helical. – The charged particle will spiral around the magnetic field lines. Phys 221 Spring 2014 Lecture 09 24 Summary: Motion of a Charged Particle • If a charged particle has a velocity parallel to the magnetic field, the magnetic force on the particle is zero. • If a charged particle is moving perpendicular to a constant magnetic field, the particle will move in a circle. • If a charged particle is moving with a velocity at some angle between 0°and 90°, it will spiral around the magnetic field lines. Phys 221 Spring 2014 Lecture 09 25