1. Currents and Magnetism Physics 102: Lecture 09

4. force is zero out of the page into the page Here  = 0 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? B I L  F = I B Lsin  a b c d B I

5. force is zero out of the page into the page 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. What is the direction of the force on section b-c of the wire? a b c d B I F

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

7. force is zero out of the page into the page 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. What is the direction of the force on section d-a of the wire? a b c d B I F

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

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

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

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

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

15. A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v Compare magnitude of 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) ACT/Preflight 9.6 q q v I v (a) r • • r (b) F F

16. 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

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

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(  ) Direction Parallel E Perpendicular to v,B Field Lines Opposites Charges Attract Currents Repel +

19. 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 ACT: Force between Wires

21. (1) Attractive (2) Zero (3) Repulsive ACT: The force between the two solenoids is …

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