Lect09 handout
- 1. Currents and Magnetism Physics 102: Lecture 09
- 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. 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 v B sin( ) = (q/t) (vt) B sin( ) = I L B sin( ) Out of the page! B v L = vt B I = q/t + + + +
- 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
- 10. ACT: Torque on Current Loop What is the torque on the loop below? < IAB = IAB > IAB x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
- 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)
- 14. Currents create magnetic fields Straight wire carrying current I generates a field B at a distance r: Magnitude Direction “ Right-hand rule 2”: Thumb of right hand along I Fingers of right hand along r Out-of-palm points along B “ Permeability of free space” (similar to 0 for electricity) Note: there are different versions of RHR I (out of page) B field circles wire B r
- 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
- 20. B I B is uniform everywhere inside of solenoid: n is the number of turns of wire/meter (n = N/L) B field lines look like bar magnet! Solenoid has N and S poles! Solenoids Magnitude Direction Use “Right-hand rule 2” A solenoid consists of N loops of wire B I
- 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
Editor's Notes
- #2: 1
- #4: Use large right hand. Then do demo 184.
- #5: Demo 253 Prop for forces on loop
- #6: Demo 253 Prop for forces on loop
- #7: Demo 253 Prop for forces on loop
- #8: Demo 253 Prop for forces on loop
- #9: 86% got that the net force was zero, but then 65% thought it wouldn’t move. Could be confusion about move vs spin. Demo 68: Big orange magnet and flip coil
- #10: 86% got that the net force was zero, but then 65% thought it wouldn’t move. Could be confusion about move vs spin. Demo 68: Big orange magnet and flip coil
- #12: 86% got that the net force was zero, but then 65% thought it wouldn’t move. Could be confusion about move vs spin. Demo 68: Big orange magnet and flip coil
- #16: Hint: think about magnitude and direction of magnetic field in each case.
- #18: Demo 740: force between two wires