Currents and Magnetism

1. 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, 3-5 PM, Rm. 141 • I will work through HE1 from last semester (fall ‘10) • To be most useful, you should work the exam yourself prior to the review

2. Summary of Today • Last time: • 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

3. 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) B v q + • 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!

4. Preflight 9.1 c d B  I B L I F=IBLsin 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? 60% 25% 15% force is zero out of the page into the page

5. Preflight 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. F What is the direction of the force on section b-c of the wire? 8% 20% 72% force is zero out of the page into the page

6. Force on loop c d B  I B L I F=IBLsin 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  = 180° Force on section c-d is zero! Same as a-b

7. ACT: Force on loop (cont’d) 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. F What is the direction of the force on section d-a of the wire? force is zero out of the page into the page

8. Torque on Current Loop in B field c d B I b a F d c a F b Look from here B F F The loop will spin in place! Preflights 9.3, 9.4: Net force on loop is zero. But the net torque is not!

9. Torque on Current Loop F d c a F b The loop will spin in place! Recall from Phys 101: F q B B w F L d F a d F Force on sections b-c and a-d: F = IBw B a Torque on loop is t= LF sin(q) = ILwBsin(q) B c c Lw = A ! b F  Torque is: b F

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

11. Torque on Current Loop It is useful to define normal vector⊥ to loop F F normal F d f f normal q a normal normal S N B B B f=0 f=0 F f = 180 – q d c F a b F F B Note torque will align normal parallel to B like a magnetic dipole! c If there are N loops: Torque is: Even if loop is not rectangular, as long as it is flat b F

12. Orbits of electrons “spin” Current loops act like dipoles Electron orbit and “spin” are current loops Why some materials are magnetic Nuclear Magnetic Resonance (NMR) and MRI

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

14. Currents create magnetic fields • Straight wire carrying current I generates a field B at a distance r: Magnitude “Permeability of free space” (similar to e0 for electricity) B • “Right-hand rule 2”: • Thumb of right hand along I • Fingers of right hand along r • Out-of-palm points along B r Direction I(out of page) B field circles wire Note: there are different versions of RHR

15. F F 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 B v q q v • • (b) (a) r r I Compare magnitude of magnetic force on q in (a) vs. (b) 34% 50% 16% a) has the larger force b) has the larger force c) force is the same for (a) and (b) Same Same Same magnitude Different directions q = 90 for (a) and (b)!

16. ACT: Adding Magnetic Fields Two long wires carry opposite current B 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

17. B B F F Example Force between current-carrying wires Currents in same direction Currents opposite direction I towards us I towards us Another I towards us Another I away from us Currents in same direction attract! Currents in opposite direction repel!

18. + 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

19. 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

20. Solenoids • A solenoid consists of N loops of wire Magnitude B is uniform everywhere inside of solenoid: n is the number of turns of wire/meter (n = N/L) N S • Use “Right-hand rule 2” Direction B I B field lines look like bar magnet! Solenoid has N and S poles! I B

21. 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.

22. Summary of Right-Hand Rules Alternate RHR 1 RHR 2 Force on moving q B field from current I Straight wire I Solenoid B r I B I