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I'm stuck on solving a linear quadrupole problem

  1. Mar 4, 2017 #1
    1. The problem statement, all variables and given/known data
    [ upload_2017-3-5_2-2-29.png

    2. Relevant equations

    I found this is about linear quadrupole and these are potential of it.
    upload_2017-3-5_2-5-27.png

    upload_2017-3-5_2-6-34.png


    3. The attempt at a solution
    So, i solve the problem (a) by using potential.
    KakaoTalk_20170305_021357511.jpg
    This is what i've done, i'm not sure if it is right though.


    And i have no idea how can i solve (b),(c) problems.
     
  2. jcsd
  3. Mar 4, 2017 #2
    For part (a) I wonder if you were expected to do simple electrostatics and geometry--adding up the single-particle fields, and doing first-order calculations for the distances. (I note that in your derivation you didn't insert the unit vectors until the last steps, so technically you're equating vectors to scalars.)

    For (b) I don't know what they mean by a "singular" charge density, but perhaps they're thinking of something like p-orbitals.

    For (c) I think this is definitely a case of simple electrostatics and geometry. Define a uniform electric field along a general direction (by symmetry this just means defining one angle) and work out the force on each charge separately; add up the results. The torque will be related to the difference in forces on the three charges (actually only the outer two are important).
     
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