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haganmc

  • 3 years ago

Show that an infinite line of charge with linear charge density lamda exerts an attractive force on an electric dipole with magnitude F = (2)(Lamda)(p) / (4)(pie)(Epsilon knot)(r^2). Assume that r is much larger than the charge separation in the dipole.

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  1. Algebraic!
    • 3 years ago
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    http://web.mit.edu/6.013_book/www/chapter11/11.8.html

  2. haganmc
    • 3 years ago
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    What part of this is the answer?

  3. haganmc
    • 3 years ago
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    I don't understand what the answer is

  4. Algebraic!
    • 3 years ago
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    start with the field of an infinite line of charge, what is that?

  5. haganmc
    • 3 years ago
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    E= 1/(4pi€.) * ( 2(lambda))/r. Then what do I do?

  6. Algebraic!
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    differentiate and multiply by p :)

  7. haganmc
    • 3 years ago
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    How would I differentiate? By dx?

  8. Algebraic!
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    did you look over the "force on a dipole" section?

  9. Algebraic!
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    Is the derivation clear?

  10. Algebraic!
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    r

  11. haganmc
    • 3 years ago
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    Yes. I think. Lol

  12. haganmc
    • 3 years ago
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    Do I differentiate or integrate?

  13. Algebraic!
    • 3 years ago
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    differentiate that upside down triangle is the gradient (space derivative)

  14. Algebraic!
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    here everything only depends on r, no x's y's or z's needed to characterize the problem...

  15. Algebraic!
    • 3 years ago
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    so the gradient is just the derivative with respect to r

  16. haganmc
    • 3 years ago
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    Differintiating will get rid of r

  17. Algebraic!
    • 3 years ago
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    nope. r is the variable.

  18. Algebraic!
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    what's the derivative of 1/r with respect to r?

  19. Algebraic!
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    \[-1/r ^{2}\]

  20. haganmc
    • 3 years ago
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    Okay I got it. Is the final answer suppose to be negative?

  21. Algebraic!
    • 3 years ago
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    all the rest of the terms are constants, they stay unchanged... multiply by the dipole moment (p) and you're done...

  22. Algebraic!
    • 3 years ago
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    yes negative r hat is towards the center so it's an attractive force...

  23. haganmc
    • 3 years ago
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    Oh now it makes sense thank you so much!! I may pass my quiz tomorrow now!

  24. Algebraic!
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    Hope it helped:) gl on the quiz!

  25. haganmc
    • 3 years ago
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    Thanks

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