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Currents and Magnetism

Learn about forces on moving charges, direction of force in magnetic fields, torque on current loops, and more in Physics 102 Lecture 9.

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Currents and Magnetism

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  1. Physics 102:Lecture 09 Currents and Magnetism • Today’s lecture will cover Textbook Sections 19.6-8 Physics 102: Lecture 9, Slide 1

  2. B v I = q/t + + + + L = vt Force of B-field on Current • Force on 1 moving charge: • F = q v B sin(q) • Out of the page (RHR) v q + • Force on many moving charges: • F = (q/t)(vt)B sin(q) • = I L B sin(q) • Out of the page! Physics 102: Lecture 9, Slide 2

  3. Preflight 9.1, 9.2 C D B I B A 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. What is the direction of the force on section A-B of the wire? force is zero out of the page into the 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 Physics 102: Lecture 9, Slide 3

  4. Preflight 9.1 C D B  I B L I F=ILBsin B A 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. 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 Physics 102: Lecture 9, Slide 4

  5. Preflight 9.2 F C D I B F B I B A X 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. 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 Physics 102: Lecture 9, Slide 5

  6. Preflight 9.1 C D B  I B L I F=ILBsin B A 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. 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 Physics 102: Lecture 9, Slide 6

  7. Preflight 9.2 F C D I B F B I B A X 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. 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 Physics 102: Lecture 9, Slide 7

  8. Torque on Current Loop in B field C F D F • B I B A F C D X A F B Look from here The loop will ___________ Preflights 9.3, 9.4 Net force on loop is _______. The net torque is __________! Physics 102: Lecture 9, Slide 8

  9. Torque on Current Loop in B field C F D F • B I B A F C D X A F B Look from here The loop will spin in place! Preflights 9.3, 9.4 Net force on loop is zero. But the net torque is not! Physics 102: Lecture 9, Slide 9

  10. Torque on Current Loop in B field f C F D F • W B I B A L F C D X A F B Force on sections B-C and A-D: F = Torqueon loop is t= 2 x (L/2) F sin(f) = (length x width = area) LW = A !  Torque is t = Physics 102: Lecture 9, Slide 10

  11. Torque on Current Loop in B field f C F D F • W B I B A L F C D X A F B L/2 L/2 Force on sections B-C and A-D: F = IBW Torqueon loop is t= 2 x (L/2) F sin(f) = ILWB sin(f) (length x width = area) LW = A !  Torque is t = I A B sin(f) Physics 102: Lecture 9, Slide 11

  12. normal F f D B A between normal and B C B F (areaof loop) Torque on Current Loop Magnitude: t = IAB sinf Direction: Torquetries to line up thenormalwithB! (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 AB sinf. N # of loops Physics 102: Lecture 9, Slide 12

  13. B B I I (2) ACT: Torque (1) Compare the torque on loop 1 and 2 which have identical area, and current. 1) t1 > t2 2) t1 = t2 3) t1 < t2 Physics 102: Lecture 9, Slide 13

  14. B B I I (2) ACT: Torque (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 Physics 102: Lecture 9, Slide 14

  15. Lines of B Currents Create B Fields Magnitude of B a distance r from (straight) wire: B Here’s a current-carrying wire. CurrentIOUT of page. r • r = distance from wire Right-Hand Rule, part deux (partie two??)! Thumb: along ______ Fingers: curl along _________ Palm: gives _____ Physics 102: Lecture 9, Slide 15

  16. CurrentIOUT • Lines of B Currents Create B Fields Magnitude: B r r = distance from wire Right-Hand Rule, part deux! Thumb: along I Fingers: curl along B field lines Physics 102: Lecture 9, Slide 16

  17. Right Hand Rule Part 2! Fingers give B! I wire http://www4.ncsu.edu/~rwchabay/emimovies/right-ha.html Physics 102: Lecture 9, Slide 17

  18. F F v v • • (b) (a) r r I Preflight 9.6 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v Compare magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) Physics 102: Lecture 9, Slide 18

  19. B same F F • same v v • • (b) (a) r r I Preflight 9.6 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v Compare magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) θ is angle between v and B (θ = 90° in both cases) Physics 102: Lecture 9, Slide 19

  20. ACT: Adding Magnetic Fields Two long wires carry opposite current 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 Physics 102: Lecture 9, Slide 20

  21. 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 Physics 102: Lecture 9, Slide 21

  22. B B Another I towards us • I towards us •  Another I away from us Force between current-carrying wires I towards us • Conclusion: Currents in same direction ____________! Conclusion: Currents in opposite direction ____________! Note: this is different from the Coulomb force between like or unlike charges. Physics 102: Lecture 9, Slide 22

  23. B B Another I towards us F • I towards us F •  Another I away from us Force between current-carrying wires I towards us • Conclusion: Currents in same direction attract! Conclusion: Currents in opposite direction repel! Note: this is different from the Coulomb force between like or unlike charges. Physics 102: Lecture 9, Slide 23

  24. 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 ChargesAttract Currents Repel Physics 102: Lecture 9, Slide 24

  25. B Field Inside Solenoids Magnitude of Field anywhere insideof solenoid :B=m0nI 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) Right-Hand Rule gives Direction: Thumb - along I Fingers – curl into interior of solenoid Palm – gives B Magnetic field lines look like bar magnet! Solenoid has N and S poles! Physics 102: Lecture 9, Slide 25

  26. B Field Inside Solenoids Magnitude of Field anywhere insideof solenoid :B=m0nI 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) Right-Hand Rule gives Direction: Thumb - along I Fingers – curl into interior of solenoid Palm – gives B Magnetic field lines look like bar magnet! Solenoid has N and S poles! Physics 102: Lecture 9, Slide 26

  27. Preflight 9.8 What is the direction of the magnetic field produced by these solenoids? • to the Right (2) to the Left ACT: B Field Inside Solenoids What is the net force between the two solenoids? (1) Attractive (2) Zero (3) Repulsive Physics 102: Lecture 9, Slide 27

  28. Preflight 9.8 What is the direction of the magnetic field produced by these solenoids? • to the Right • to the Left Right Hand Rule! Physics 102: Lecture 9, Slide 28

  29. ACT: B Field Inside Solenoids What is the net force between the two solenoids? (1) Attractive (2) Zero (3) Repulsive Look at field lines, opposites attract. Look at currents, same direction attract. Physics 102: Lecture 9, Slide 29

  30. See you next lecture! • Read Ch. 20.1, 3-4 • Lots of cool demos next class! Physics 102: Lecture 9, Slide 30

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