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MULTIPOLE EXPANSION

MULTIPOLE EXPANSION. Class Activities: Multipole. Dipole moment - off center. MD6.1. The dipole moment, . +q. r 1. d. x. r 2. -q. Dipole moment - off center. MD6.1. +q. d. -q. r 1. y. r 2. x. A small dipole (dipole moment p=qd) points in the z direction. We have derived.

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MULTIPOLE EXPANSION

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  1. MULTIPOLE EXPANSION

  2. Class Activities: Multipole

  3. Dipole moment - off center MD6.1 The dipole moment, +q r1 d x r2 -q

  4. Dipole moment - off center MD6.1 +q d -q r1 y r2 x

  5. A small dipole (dipole moment p=qd) points in the z direction. We have derived 3.22a Which of the following is correct (and "coordinate free")? A) B) C) D) E) None of these

  6. An ideal dipole (tiny dipole moment p=qd) points in the z direction. We have derived 3.22b Sketch this E field... (What would change if the dipole separation d was not so tiny?)

  7. 3.22b Sketch this E field…

  8. For a dipole at the origin pointing in the z-direction, we have derived z + d x - MD6 - 2 For the dipole p = q d shown, what does the formula predict for the direction of E(r=0)? • Down B) Up C) some other direction • D) The formula doesn't apply.

  9. An ideal dipole (tiny dipole moment p=qd) points in the z direction. We have derived 3.22b (What would change if the dipole separation d was not so tiny?)

  10. StreamPlot[ {(3*x*y)/(Sqrt[x^2 + y^2])^5, (2*y*y – x*x)/(Sqrt[x^2 + y^2])^5}, {x, -2, 2}, {y, -2, 2}]

  11. What is the magnitude of the dipole moment of this charge distribution? 3.27 qd B) 2qd C) 3qd D) 4qd E) It's not determined (To think about: How does V(r) behave as |r| gets large?)

  12. Dipole moment - off center MD6.1 What is the dipole moment of this system? (Note: it is NOT overall neutral!) +2q d 0 x -q

  13. Dipole moment - off center MD6.1 What is the dipole moment of this system? (Note: same as last question, just shifted in z!) +2q d/2 r1 d 0 x r2 d/2 -q

  14. You have a physical dipole, +q and -q a finite distance d apart. When can you use the expression: 3.22c A) This is an exact expression everywhere. B) It's valid for large r C) It's valid for small r D) ?

  15. You have a physical dipole, +q and -q, a finite distance d apart. When can you use the expression 3.22 d A) This is an exact expression everywhere. B) It's valid for large r C) It's valid for small r D) ?

  16. Which charge distributions below produce a potential which looks like C/r2 when you are far away? 3.25 E) None of these, or more than one of these! (Note: for any which you did not select, how DO they behave at large r?)

  17. Which charge distributions below produce a potential which looks like C/r2 when you are far away? 3.26 E) None of these, or more than one of these! (Note: for any which you did not select, how DO they behave at large r?)

  18. 3.28 In which situation is the dipole term the leading non-zero contribution to the potential? A) A and C B) B and D C) only E D) A and E E) Some other combo

  19. Electric properties of matter No flies were harmed in the process

  20. Let me know how far along you are: • DONE with page 1 • DONE with page 2 • DONE with page 3!

  21. On paper (don’t forget your name!) in your own words (by yourself):What is the idea behind the multipole expansion? What does it accomplish?In what limits/cases is it useful?

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