Currents and Magnetism 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 last semester (fall ‘09) To be most useful, you should work the exam yourself prior to the review 1

Summary of Today Last time: Today: Magnetic forces on moving charge magnitude F=qvBsin() direction: right-hand-rule Today: 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(q) Out of the page (RHR) B q v + Force on many moving charges: F = q v B sin(q) = (q/t) (vt) B sin(q) = I L B sin(q) Out of the page! v L = vt B I = q/t + Use large right hand. Then do demo 184. 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 I L  F=IBLsin a b c d B I Here  = 0. Demo 253 Prop for forces on loop What is the direction of the force on section a-b of the wire? force is zero 61% out of the page 23% into the page 16% demo 253 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. a b c d B I X F What is the direction of the force on section b-c of the wire? force is zero 9% out of the page 26% into the page 66% 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 I L  F=IBLsin a b c d B I Here  = 180º I B Force on c-d is Zero! same as for a-b! 10

ACT/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. a b c d B I • F (a) force is zero (b) out of the page (c) into the page 11

Torque on Current Loop in B field a b c d B I X F • a b c d F Look from here The loop will spin in place! 86% got that the net force was zero, but then 65% thought it wouldn’t move. Could be confusion about move vs spin. Demo 68: Big orange magnet and flip coil 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.” 12 demo 68

Torque on Current Loop in B field W L a b c d B I X F • a b c d F f 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) LW = A !  Torque is t = I A B sin(f) 14

ACT: Torque on Current Loop What is the torque on the loop below? t < IAB t = IAB t > IAB x x x x x x x x x x x x x x x x t = 0 16

Torque on Current Loop N t = I A B sinf Direction: normal Magnitude: f Orbits of electrons “spin” Magnitude: t = I A B sinf between normal and B Direction: 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 = I A B sinf. N (area of loop) # of loops 20

ACT: Torque t = I A B sinf B B I (2) I (1) Compare the torque on loop 1 and 2 which have identical area, and current. Area points out of page for both! f = 90 degrees 1) t1 > t2 2) t1 = t2 3) t1 < t2 t = I A B sinf 23

Currents Create B Fields Magnitude: Lines of B B Current I OUT • r r = distance from wire Right-Hand Rule, part deux! Thumb: on I Fingers: position you want to know B at Palm: gives B 25

Fingers give B! Right Hand Rule Part 2! I wire 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 I (a) r • (b) F same • B Compare magnetic force on q in (a) vs. (b) 31% 50% 19% a) has the larger force b) has the larger force c) force is the same for (a) and (b) Hint: think about magnitude and direction of magnetic field in each case. 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 • • Another I towards us F Conclusion: Currents in same direction attract! • I towards us B F  Another I away from us Demo 740: force between two wires Conclusion: Currents in opposite direction repel! demo 740 35

Comparison: Electric Field vs. Magnetic Field Electric Magnetic Source Charges Moving Charges Acts on Charges Moving Charges Force F = Eq F = q v B sin(q) Direction Parallel E Perpendicular to v,B Field Lines Opposites Charges Attract Currents Repel 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 : B=m0 n I n is the number of turns of wire/meter on solenoid. m0 = 4p 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 Demo 183: overhead and iron filings w/solenoid Magnetic field lines look like bar magnet! Solenoid has N and S poles! demo 183 43

ACT: The force between the two solenoids is … (1) Attractive (2) Zero (3) Repulsive Look at field lines, opposites attract. Look at currents, same direction attract. 48

See you Monday! 50