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Currents and Magnetism

Physics 1161: Lecture 13. Currents and Magnetism. Textbook Sections 22-4 – 22-7. 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 )

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Currents and Magnetism

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  1. Physics 1161:Lecture 13 Currents and Magnetism • Textbook Sections 22-4 – 22-7

  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!

  3. Preflight 13.1 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 45% 36% 18%

  4. Preflight 13.2 F C D 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. v B Palm into page. F What is the direction of the force on section B-C of the wire? force is zero out of the page into the page 9% 45% 45%

  5. Torque on Current Loop in B field F C D F • B I B A F C D X A F B Look from here The loop will spin in place! Preflights 13.3, 13.4 Net force on loop is zero. But the net torque is not! 91%

  6. 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 =

  7. 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)

  8. 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

  9. Compare the torque on loop 1 and 2 which have identical area, and current. • t1 > t2 • t1 = t2 • t1 < t2

  10. Compare the torque on loop 1 and 2 which have identical area, and current. • t1 > t2 • t1 = t2 • t1 < t2 t = I A B sinf Area points out of page for both! f = 90 degrees

  11. CurrentIOUT • Lines of B Currents Create B Fields Magnitude: B r r = distance from wire Right-Hand Rule-2 Thumb: along I Fingers: curl along B field lines

  12. Right Hand Rule 2! Fingers give B! I wire

  13. B same F F • same v v • • (b) (a) r r I Preflight 13.6 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 force is the same for (a) and (b) 27% 59% 14% θ is angle between v and B (θ = 90° in both cases)

  14. 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”? • Left • Right • Up • Down • Zero x x

  15. 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”? B • Left • Right • Up • Down • Zero x x

  16. 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.

  17. 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

  18. Magnetic Fields of Currents • http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfie.html#c1

  19. Right Hand Rule 3Magnetic Field of Solenoid

  20. 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 for loop/solenoid Fingers – curl around coil in direction of conventional (+) current Thumb - points in direction of B along axis Magnetic field lines look like bar magnet! Solenoid has N and S poles!

  21. Preflight 13.8 What is the direction of the magnetic field produced by these solenoids? • to the Right • to the Left 76% 24% Right Hand Rule!

  22. What is the net force between the two solenoids? • Attractive • Zero • Repulsive

  23. What is the net force between the two solenoids? • Attractive • Zero • Repulsive Look at field lines, opposites attract. Look at currents, same direction attract.

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