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Physics 2112 Unit 15

Physics 2112 Unit 15. Today’s Concept: Ampere’s Law. Ampere’s Law. We know for an infinite current carrying wire. But what is 2 p R ? Circumference of circle!. Ampere’s Law. Any closed loop. Current enclosed by that closed loop. Checkpoint 1A.

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Physics 2112 Unit 15

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  1. Physics 2112Unit 15 Today’s Concept: Ampere’s Law

  2. Ampere’s Law We know for an infinite current carrying wire But what is 2pR? Circumference of circle!

  3. Ampere’s Law Any closed loop Current enclosed by that closed loop

  4. Checkpoint 1A Two loops are placed near identical current carrying wires as shown in Case 1 and Case 2 below. • For which loop is ∫B·dl greater? • Case 1 • Case 2 • The integral is the same for both

  5. Checkpoint 1B Two loops are placed near identical current carrying wires as shown in Case 1 and Case 2 below. • For which loop is ∫B·dl greater? • Case 1 • Case 2 • The integral is the same for both

  6. Checkpoint 1C Two loops are placed near current carrying wires as shown in Case 1 and Case 2 below. In both cases the direction of the current in the two wires are opposite to each other. • For which loop is ∫B·dl greater? • Case 1 • Case 2 • The integral is the same for both

  7. Example 15.1 (B field from a thick wire) A wire with a radius of r=1cm has a uniform current of 1A flowing through it. What is the B field 1 meter from the center of the wire? What is the B field 0.5cm from the center of the wire?

  8. Example 15.1 (graph) A wire with a radius of r=1cm has a uniform current of 1A flowing through it. X X XX X XXXX X X XX X XXXX B r

  9. CheckPoint 2A An infinitely long hollow conducting tube carries current I in the direction shown. X • What is the direction of the magnetic field inside the tube? • clockwise • counterclockwise • radially inward to the center • radially outward from the center • the magnetic field is zero

  10. Why is that? X X

  11. Example 15.3 (Pipe of current) y An infinitely long cylindrical shell carries a uniformly distributed current of 5A out of the screen. The inner radius is a=4cm and outer radius=8cm What is B at r = 2cm? What is B at r = 6cm? What is B at r = 16cm? I a x b

  12. Example 15.3 (Pipe of current) • Conceptual Analysis • Complete cylindrical symmetry (can only depend on r) can use Ampere’s law to calculate B • Strategic Analysis • Calculate B for the three regions separately: • 1) r < a • 2) a < r < b • 3) r > b For circular path concentric with shell.

  13. Example 15.2 (Two thick wires) Two thick cables both of radius R and length L carry a current, I, side-by-side as shown to the left. The left cable has the current into the screen and the right cable has the current out of the screen. A B C X D What is the magnetic field at points A, B, C and D? - A is at the center of the left cable - B is a distance R/2 from the center of the left cable - C is at the point where the cables touch. - D is the bottom of the left cable

  14. The Plan What is the magnetic field at points A, B, C and D? A B C X D • Conceptual Analysis • use Ampere’s law to calculate B from each cable separately • Strategic Analysis • Note direction of B from each cable at each point. • AddBlike vectors

  15. Sign of the dot product Iintoscreen

  16. Ampere’s Law dl B dl B B dl

  17. Sign of the dot product B dl dl B B dl

  18. Sign of the dot product B dl B dl dl B

  19. B Field in Solenoid ~cancel out . . . . X X X X add up

  20. B Field in Solenoid . . . . . . . . X X X X X X X X L n = turns per unit length (Ideal Solenoid L>>>r)

  21. Solenoid   Bar Magnet

  22. CheckPoint2B A current carrying wire is wrapped around cardboard tube as shown below. • In which direction does the magnetic field point inside the tube? • left • right • up • down • out of the screen • into the screen

  23. Example 15.3 (B from Solenoid) A long thin solenoid consists of 500 turns of wire carrying 1.5A. It has a length of 250cm and a radius of 1cm. What is the magnetic field in the exact center of the coil? What is the contribution to this field from the 250th coil (the center coil)?

  24. Make Sense? . . . . . . . . X X X X X X X X Note: • B250/Btot= 0.024 (1/500 = 0.002) • So closest coil contributes over 10 tens more than average coil. Make sense?

  25. When does “Loop”  “Solenoid”?

  26. A hint…..

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