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

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

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

4. Physics 102: Lecture 9, Slide 4 force is zero out of the page into the page B I L  F=ILBsin  Here  = 0. A B C D B I 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. What is the direction of the force on section A-B of the wire?

5. Physics 102: Lecture 9, Slide 5 What is the direction of the force on section B-C of the wire? force is zero out of the page into the page Palm into page. B F I A B C D B I X F 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.

6. Physics 102: Lecture 9, Slide 6 force is zero out of the page into the page B I L  F=ILBsin  Here  = 0. A B C D B I 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. What is the direction of the force on section A-B of the wire?

7. Physics 102: Lecture 9, Slide 7 What is the direction of the force on section B-C of the wire? force is zero out of the page into the page Palm into page. B F I A B C D B I X F 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.

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

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

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

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

12. Physics 102: Lecture 9, Slide 12 Torque tries to line up the normal with B! (when normal lines up with B,  =0, so  =0! ) Even if the loop is not rectangular, as long as it is flat:  = I A B sin   (area of loop) Magnitude:  = I A B sin  Direction: N # of loops A B C D B normal  F F Torque on Current Loop between normal and B

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

14. Physics 102: Lecture 9, Slide 14 B Compare the torque on loop 1 and 2 which have identical area, and current. I ACT: Torque (1) B I (2) 1)  1 >  2 2)  1 =  2 3)  1 <  2 Area points out of page for both!  = 90 degrees  = I A B sin 

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

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

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

18. Physics 102: Lecture 9, Slide 18 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) v I v (a) r r (b) F F Preflight 9.6

19. Physics 102: Lecture 9, Slide 19 θ is angle between v and B ( θ = 90° in both cases) 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) same B v I v (a) r r (b) F F Preflight 9.6

20. Physics 102: Lecture 9, Slide 20 Two long wires carry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x ACT: Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero x

21. Physics 102: Lecture 9, Slide 21 Two long wires carry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x ACT: Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero B x

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

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

24. Physics 102: Lecture 9, Slide 24 Comparison: Electric Field vs. Magnetic Field ElectricMagnetic Source ChargesMoving Charges Acts on Charges Moving Charges Force F = Eq F = q v B sin(  ) Direction Parallel EPerpendicular to v,B Field Lines Opposites Charges AttractCurrents Repel

25. Physics 102: Lecture 9, Slide 25 B Field Inside Solenoids Magnitude of Field anywhere inside of solenoid : B=  0 n I Right-Hand Rule gives Direction: Thumb - along I Fingers – curl into interior of solenoid Palm – gives B n is the number of turns of wire/meter on solenoid.   = 4  x10 -7 T m /A (Note: N is the total number of turns, n = N / L) Magnetic field lines look like bar magnet! Solenoid has N and S poles!

26. Physics 102: Lecture 9, Slide 26 B Field Inside Solenoids Magnitude of Field anywhere inside of solenoid : B=  0 n I Right-Hand Rule gives Direction: Thumb - along I Fingers – curl into interior of solenoid Palm – gives B n is the number of turns of wire/meter on solenoid.   = 4  x10 -7 T m /A (Note: N is the total number of turns, n = N / L) Magnetic field lines look like bar magnet! Solenoid has N and S poles!

27. Physics 102: Lecture 9, Slide 27 What is the direction of the magnetic field produced by these solenoids? Preflight 9.8 (1)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

28. Physics 102: Lecture 9, Slide 28 What is the direction of the magnetic field produced by these solenoids? Right Hand Rule! Preflight 9.8 (1)to the Right (2)to the Left

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

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