Physics 102 Lecture 09 Currents and Magnetism Exam

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 HE 1 from last semester (fall ‘ 09) – To be most useful, you should work the exam yourself prior to the review

Summary of Today • Last time: – Magnetic forces on moving charge • magnitude F=qv. Bsin( ) • 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( ) – Out of the page (RHR) B + • Force on many moving charges: – F = q v B sin( ) = (q/t) (vt) B sin( ) = I L B sin( ) – Out of the page! Demo: 184 v B + +v I = q/t L = vt 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 L F=IBLsin Here = 0. 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. c d F X B a I b What is the direction of the force on section b-c of the wire? force is zero 9% out of the page into the page 26% 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 c d B a I b Force on c-d is Zero! I L F=IBLsin Here = 180º I B 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. c d • F B a I b (a) force is zero (b) out of the page (c) into the page 11

Torque on Current Loop in B field c d • F F X B a I F a c d b b F The loop will spin in place! Look from here Net force on loop is zero. Preflights 9. 3, 9. 4 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 F F X W B a a I 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 xxxxxxxxxxxxx xxx x x x x 16 xxx

Torque on Current Loop Magnitude: Orbits of electrons al F d t = I A B sinf Direction: norm f a between normal and B B c b “spin” 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 loop) 20

ACT: Torque B B I 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) t 1 > t 2 2) t 1 = t 2 3) t 1 < t 2 f = 90 degrees t = I A B sinf 23

Currents Create B Fields Magnitude: B Current I OUT r • 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: //www 4. 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) 31% a) has the larger force 50% b) has the larger force c) force is the same for (a) and (b) 19% same 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 • F B • 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 F = Eq Parallel E 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=m 0 n I m 0 = 4 p x 10 -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: 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