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Physics 212 Lecture 15

Physics 212 Lecture 15. Ampere’s Law. LHS:. RHS:. General Case. Infinite current-carrying wire. :05. Checkpoint 1c. Checkpoint 1a. Checkpoint 1b. I enclosed = 0. I enclosed = 0. I enclosed = I. I enclosed = 0. I enclosed = I. I enclosed = I. Practice on Enclosed Currents.

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Physics 212 Lecture 15

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  1. Physics 212 Lecture 15 Ampere’s Law

  2. LHS: RHS: General Case Infinite current-carrying wire :05

  3. Checkpoint 1c Checkpoint 1a Checkpoint 1b Ienclosed = 0 Ienclosed = 0 Ienclosed = I Ienclosed = 0 Ienclosed = I Ienclosed = I Practice on Enclosed Currents For which loop is B·dl the greatest? A. Case 1 B. Case 2 C. Same For which loop is B·dl the greatest? A. Case 1 B. Case 2 C. Same For which loop is B·dl the greatest? A. Case 1 B. Case 2 C. Same :08

  4. An infinitely long hollow conducting tube carries current I in the direction shown. Cylindrical Symmetry X X X X Enclosed Current = 0 Checkpoint 2a Check cancellations What is the direction of the magnetic field inside the tube? A. clockwise B. counterclockwise C.radially inward to the center D.radially outward from the center E. the magnetic field is zero :22

  5. Line Integrals I intoscreen :12

  6. dl B dl B B dl Ampere’s Law :14

  7. B dl B dl B dl Ampere’s Law :16

  8. B dl B dl dl B Ampere’s Law :16

  9. Which of the following current distributions would give rise to the B.dL distribution at the right? A C B :18

  10. :19

  11. :19

  12. :19

  13. Match the other two: B A :21

  14. Checkpoint 2b :22

  15. Simulation :23

  16. Solenoid n = # turns/length Several loops packed tightly together form a uniform magnetic field inside, and nearly zero magnetic field outside. 1 2 3 4 Assume a constant field inside the solenoid and zero field outside the solenoid. Apply Ampere’s law to find the magnitude of the field. :28

  17. Example Problem y For circular path concentric w/ shell An infinitely long cylindrical shell with inner radiusaand outer radiusbcarries a uniformly distributed currentIout of the screen. Sketch |B| as a function of r. I a x • Conceptual Analysis • Complete cylindrical symmetry (can only depend on r) can use Ampere’s law to calculate B • B field can only be clockwise, counterclockwise or zero! b • Calculate B for the three regions separately: • 1) r < a • 2) a < r < b • 3) r > b :31

  18. Example Problem y so 0 I r a b x What does |B| look like for r < a ? (A) (B)(C) :33

  19. Example Problem y I I r a b x What does |B| look like for r > b ? (A) (B)(C) :35

  20. Example Problem y LHS: RHS: What does |B| look like for r > b ? dl I r B a b x (A) (B)(C) :36

  21. Example Problem y j = I / area I What is the current density j (Amp/m2) in the conductor? a b x (A) (B)(C) :40

  22. Example Problem y I r a b x What does |B| look like for a < r < b ? (A) (B)(C) :43

  23. Example Problem y Starts at 0 and increases almost linearly What does |B| look like for a < r < b ? I r a b x (A) (B)(C) :45

  24. Example Problem y An infinitely long cylindrical shell with inner radiusaand outer radiusbcarries a uniformly distributed currentIout of the screen. Sketch |B| as a function of r. I a x b :48

  25. Follow-Up y X Add an infinite wire along the z axis carrying current I0. What must be true about I0 such that there is some value of r, a < r < b, such that B(r) = 0 ? I a I0 x A) |I0| > |I| AND I0 into screen b B) |I0| > |I| AND I0 out of screen C) |I0| < |I| AND I0 into screen D) |I0| < |I| AND I0 out of screen E) There is no current I0 that can produce B = 0 there B will be zero if total current enclosed = 0 :48

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