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Physics 102: Lecture 09 Currents and Magnetism • • • • Exam 1 Monday night Conflicts, etc.—see course home page Be sure to bring your ID and go to correct room Review Sunday, 3-4:30 PM, rm. 141 – I will work through HE1 from Fall 2007 – To be most useful, you should work the exam yourself prior to the review Summary of Today • Last time – Magnetic field lines – Magnetic forces on moving charge • magnitude F=qvBsin() • direction: right-hand-rule • Magnetic forces on currents and current loops • Magnetic fields due to currents – long straight wire – solenoid Force of B-field on Current • Force on 1 moving charge: – F = q v B sin() – Out of the page (RHR) + v • Force on many moving charges: – F = (q/t)(vt)B sin() = I L B sin() – Out of the page! B + + + +v I = q/t L = vt Demo: 184 7 Preflight 9.1 A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. B c d B a I b I F=IBLsin Here = 0. What is the direction of the force on section A-B of the wire? force is zero out of the page into the page demo 253 46% 36% 18% 8 Preflight 9.2 A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. I c d X F B a I b Palm into page. What is the direction of the force on section B-C of the wire? force is zero out of the page into the page 13% 29% 58% 9 Force on Loop A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. B c d B a I b Force on C-D is Zero! I F=IBLsin Here = 180º I B same as for A-B! 10 Force on Loop (cont’d) A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. c d B a I b F I • F Palm out of page. Force on A-D is out of the page. 11 Torque on Current Loop in B field c d • F X F B F a a I c d b b F The loop will spin in place! Look from here Preflights 9.3, 9.4 Net force on loop is zero. But the net torque is not! “As long as the net force on the loop is zero, there is no reason for the loop to move.” demo 68 12 Torque on Current Loop in B field c d • F X F W F B a I a c d f b F b L Force on sections B-C and A-D: F = IBW Torque on loop is t = L F sin(f) = ILWB sin(f) (length x width = area) Torque is LW = A ! t = I A B sin(f) 14 ACT: Torque on Current Loop What is the torque on the loop below? 1) t < IAB 2) t = IAB 3) t > IAB t=0 xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx 16 Torque on Current Loop Magnitude: F t = I A B sinf Direction: between normal and B f B F Torque tries to line up the normal with B! (when normal lines up with B, f=0, so t=0! ) Even if the loop is not rectangular, as long as it is flat: t = N I A B sinf. # of loops (area of 20 ACT: Torque B B I (1) (2) Compare the torque on loop 1 and 2 which have identical area, and current. Area points out of page for both! 1) t1 > t2 2) t1 = t2 3) t1 < t2 f = 90 degrees t = I A B sinf 23 Currents Create B Fields Magnitude: 0I B 2r B Current I OUT r 0 4 10 7 Tm / A • r = distance from wire Right-Hand Rule, part deux! Thumb: Fingers: Palm: Lines of B on I position you want to know B at gives B 25 Right Hand Rule Part 2! I wire Fingers give B! http://www4.ncsu.edu/~rwchabay/emimovies/right-ha.html ACT/Preflight 9.6 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v v v • (a) F r B• (b) r • F I Compare magnetic force on q in (a) vs. (b) 33% a) has the larger force 51% b) has the larger force c) force is the same for (a) and (b) 16% 0I same B 2r same F qvB sin Different directions 28 ACT: Adding Magnetic Fields Two long wires carry opposite current B x x What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? 1) Left 2) Right 3) Up 4) Down 5) Zero 32 Force between current-carrying wires I towards us • B • F Another I towards us Conclusion: Currents in same direction attract! I towards us • B F Another I away from us Conclusion: Currents in opposite direction repel! demo 740 35 Comparison: Electric Field vs. Magnetic Field Source Acts on Force Direction Electric Magnetic Charges Charges F = Eq Parallel E Moving Charges Moving Charges F = q v B sin() Perpendicular to v,B Charges Attract Currents Repel Field Lines Opposites 37 ACT: Force between Wires What is the direction of the force on the top wire, due to the two below? 1) Left 2) Right 3) Up 4) Down 5) Zero 40 B Field Inside Solenoids Magnitude of Field anywhere inside of solenoid : n is the number of turns of wire/meter on solenoid. B=0 n I 0 = 4 x10-7 T m /A (Note: N is the total number of turns, n = N / L) Another Right-Hand Rule gives Direction: Curl fingers in direction of current Thumb point in direction of B Magnetic field lines look like bar magnet! demo 183 Solenoid has N and S poles! 43 ACT: B Field Inside Solenoids (1) Attractive (2) Zero (3) Repulsive Look at field lines, opposites attract. Look at currents, same direction attract. 48 See you Monday! • Lots of cool demos! 50