Magnetic Fields & Forces

Transcription

1 Magnetic Fields & Forces Magnetic fields are prodced by crrents and permanent magnets. The smallest nit is the dipole, as we ll see. Magnetic fields exert forces on moving charges. The reslting path can is often a circle. Magnetic dipoles line p with magnetic fields. That s why compasses point north. Dipoles & Fields From the top, crrent is conterclockwise. From the bottom, crrent is clockwise.

2 (b) North and Soth S N The Smallest Unit is a Dipole The Magnetic Field of the Earth

3 Navigation 60 Sorces of the Magnetic Field Crrent Permanent Atomic loop magnet magnet Sorces of the Magnetic Field: Field of a Crrent-Carrying Wire Make yor stdy sheet now. Pt this on it. Unit: Tesla (T) µ 0 = Tim/A

4 Notation Sorces of the Magnetic Field: Field of a Crrent Loop For crrent in a coil or a loop, field lines emerge from the center of the loop and wrap arond it in a direction given by the right-hand rle for fields. Nmber of trns. For a loop, N = 1. Crrent (A) Field (T) at the center B = m 0 N 2R Radis of the loop or coil (m) FGURE The magnetic field of a crrent loop. Use the right-hand rle for fields to find the direction of the field lines. Near the wire, the field lines are almost circlar. The field emerges from the center of the loop c cand retrns arond the otside of the loop. View of loop from left side Face-on view of loop Use the STOP TO THNK 24.3 The figre shows an edge view of a crrent loop. Using what yo ve learned in Figre 24.15, which arrow gives the direction of the active field in the center of the loop? elements. D A C B

5 Sorces of the Magnetic Field: R Field of a Solenoid a coil or a loop, field lines emerge r of the loop and wrap arond it in en by the right-hand rle for fields. A solenoid is a stack of loops with the length mch greater Nmber than the radis. of trns. For a loop, N L= 1. Crrent (A) R Field (T) at the center B = m 0 N 2R Radis of the loop or coil (m) The field (T) inside a solenoid is niform. Nmber of trns B = m 0 N L Length of the solenoid (m) Crrent (A) Field is large, niform inside; essentially zero otside. Nmbers Althogh the evidence is weak, there has been some concern in recent years abot health effects from the magnetic fields generated by transmission lines. a. What is the magnetic field on the grond below a high-voltage transmission line 20 m above the grond that carries a crrent of 200 A? b. What fraction of the earth s field is this? B = µ 0 2πr Jst Checking. A. Toward the top of the screen B. Toward the bottom of the screen 03/10/13 1:53 PM

6 Jst Checking. Jst Checking. What s the direction of What the magnetic is the magnetic field at this field point? at this point? A. Toward the top of the screen B. To the right C. Toward the bottom of the screen D. To the left Adding Fields 11. Two long wires carry crrents in the directions shown in Figre Q One wire is 10 cm above the other. n which direction is the magnetic field at a point halfway between them? 12. An electron is moving in a circlar orbit in a niform magnetic A B FGURE Q24.11 C D

7 Force on a Moving Charged Particle The direction of the force The magnitde of the force F Magnitde of charge (C) Magnetic field (T) B v F = Speed of particle (m/s) 0 q 0 vb sin a Angle between v and B (24.5) n this case, F is directed p from the plane. F B v FGURE Q24.14 Jst Checking solenoid? Explain. 5. What is the initial direction of deflection for the charged particles entering the magnetic fields shown in Figre Q24.15? (a) (b) v v FGURE Q24.15 v B F F = 0 q 0 vb sin a 784 CHAPTER 24 Magnetic F = 0 q Fields 0 vb and Forces agnetic Fields and Forces Magnetic Fields Exert Forces on Crrents rce on a However, FGURE Magnetic there force is a on force a on a crrent-carrying wire that is perpendiclar to a However, there is a force on a crrent-carrying wire that is perpendiclar to a crrent-carrying magnetic wire. field, as shown in FGURE ) magnetic field, as shown in FGURE For a negative charge, the The magnitde of (a) NOTE The magnetic (b) field is an external field, created by a permanent magnet or force is in the by direction other crrents; it is the not force the field is given of the crrent NOTE Direction in The the wire. magnetic is field is an external field, created by a permanent magnet or n opposite that predicted by by Eqation 24.5 by other the right-hand rle. Eqation given crrents; by it RHR is not the field of the crrent in the wire. The direction of the force the crrent is fond by considering the force on each charge in the crrent. We model crrent as the flow of positive charge, so the righthand rle for forces applies to crrents in the same way it does for moving The direction of the force on the crrent is fond by considering the force on each charge in the crrent. We model crrent as the flow of positive charge, so the righthand of positive rle charges) for forces and yor applies index finger to crrents in the same way it does for moving F charges. With yor fingers aligned as sal, point yor right thmb in the direction of the crrent (the direction of the motion in the direction L of B. F Yor middle finger charges. is then pointing With in yor the direction fingers of aligned the force as sal, point yor right thmb in the direction F on the wire, as in FGURE 24.37c. Conseqently, of the crrent the entire (the length direction of wire within of the the B motion of positive charges) and yor index finger magnetic field experiences a force perpendiclar to both 03/10/13 the crrent 1:53 PM in the direction of B direction and the. Yor middle finger is then pointing in the direction of the force field direction, as shown in FGURE 24.37b. F on the wire, as in FGURE 24.37c. Conseqently, the entire length of wire within the B f the length of the wire B L, the crrent, or the magnetic field B is increased, then he wire carries rrent, the magnetic the magnitde of the force on the wire will magnetic also increase. field We experiences can show that a the force magnetic force on a crrent-carrying wire is given field by direction, as shown in FGURE 24.37b. perpendiclar to both the crrent direction and the d will exert a force the wire. f the length of the wire L, the crrent, or the magnetic field B is increased, then A wire is perpendiclar f the wire carries to an externally B created a crrent, the magnetic the magnitde of the force on the wire will also increase. We can show that the magnetic force on a crrent-carrying wire is given by a Crrent in wire (A) Magnetic field (T) magnetic field. field will exert a force on the wire. F wire = LB sin a (24.9) he right-hand rle L Length of wire in Angle between wire r forces applies. magnetic field (m) (c) B and magnetic field or thmb shold a Crrent in wire (A) Magnetic field (T) oint in the direction f the crrent. n many practical cases the wire will be perpendiclar to the field, so that a = 90. n F wire = LB sin a (24.9)

8 What is the direction of the force on the crrent? B B r A.! Toward the top of the screen B.! To the right C.! Toward the bottom of the screen D.! To the left Which way will the coil rotate? A.! Clockwise B.! Conterclockwise Warming Up 35. f two compasses are broght near enogh A. to each other, the magnetic fields of the compasses themselves will be larger than the B. field of the earth, and the needles will line p C. with each other. Which of the arrangements D. of two compasses shown in Figre Q24.35 is a possible stable arrangement? FGURE Q24.35

9 Nmbers Hammerhead sharks can detect magnetic fields. n one test sharks trained to get a food reward when a field was present cold nambigosly respond to the field generated by a crrent of 1.5 A in a 100 trn coil of wire wrapped arond a tank 7.5 m in diameter. a. What was the field strength at the center of the tank? b. s this field larger or smaller than the field of the earth? Nmbers A typical MR solenoid has a length of approximately 1.0 m and a diameter of 1.0 m. a. How many trns of wire are reqired to prodce a field of 1.0 T (a typical field) if the maximm crrent the wires can carry is 100 A? b. How long is the wire? Paths of Charged Particles F = qvb F = ma = m v2 r r = mv qb

10 Jst Checking For particles (positively charged) enter a region of niform magnetic field and follow the paths shown. What is the field direction? A. Toward the top of the screen B. Toward the bottom of the screen C. nto the screen D. Ot of the screen A. B. C. D. Jst Checking For particles of identical charge and mass enter a region of niform magnetic field and follow the trajectories shown in Figre Q Which particle has the highest velocity? FGURE Q24.33 A. B. C. D. Paths of Charged Particles Microwave ovens prodce the electromagnetic waves called microwaves from the rapid orbiting of free electrons in a magnetic field. The electrons orbit inside a tbe called a magnetron. They orbit at a freqency of 2.4 GHz, emitting electromagnetic waves of this freqency in the process. What is the necessary magnetic field strength?

11 Closer to Home: The Mass Spectrometer 1. Atoms are ionized and accelerated. ons of a particlar velocity are selected to enter the spectrometer. 2. ons of different masses follow paths of different radii. 2r r B Detector URE P Only ions of a particlar mass reach the exit slit and contine to the detector. Jst Checking Figre Q24.32 shows for particles moving to the right as they enter a region of niform magnetic field, directed into the paper as noted. All particles move at the same speed and have the same charge. Which particle has the largest mass? FGURE Q24.32 A. B. C. D. B Speakers Use Magnets

12 Warming Up Determine the magnetic field direction that cases the charged particles shown in Figre Q24.18 to experience the indicated magnetic forces. (a) v (b) FGURE Q24.18 F ot of page F v into page Forces Between Crrents The wires in a jmper cable carry opposite crrents, as noted. There will be a force between the wires. This force is: A.! Attractive B.! Replsive Hint: Figre ot: 1. What is the field from the pper wire at the lower wire? 2. What is the direction of this force on the crrent? The Velocity Selector What is the direction of the force de to the: a. electric field? b. magnetic field? A.!! Up B.!! Down C.!! Right D.!! Left For what velocity particle will there be no deflection? qe = qvb v = E B

13 The Velocity Selector What is the direction of the force de to the: a. electric field? b. magnetic field? What will be the motion of the particle if it travels faster than this? The Electromagnetic Flowmeter 1. Positive and negative ions flow to the right in the field of the magnets. B N S v 2. An end view shows that the magnetic force on the positive ions is to the right, and on the negative ions to the left. F neg N S V v S ot of page F pos 3. The reslting charge separation leads to a potential difference that can be measred between two electrodes. qe = qvb E = V d v = E B v = ΔV Bd s Erope + or - with respect to the US?

14 f the flow is north at 3.5 m/s, the field is tipped at a 60 angle, and an investigator places two electrodes 10 m apart, on an east-west axis, what is the measred voltage? Torqe on Dipoles Magnetic Resonance maging

15 Magnetic Materials Certain materials are ferromagnetic. Single Domain Magnetite: A possible tool for magnetic navigation? Biogenic magnetite from sockeye salmon Navigating with the Dip Angle Field along Florida coast Dip angle

16 Navigating with the Dip Angle Tests with green trtle hatchlings Trtle + Magnet = Disorientation Pink = Experimental Black = Control