Coulomb's law in vector form

Discussion in 'Physics' started by logearav, Jan 4, 2012.

  1. logearav

    Thread Starter Member

    Aug 19, 2011
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    Revered Members,
    Kindly see my attachment.
    Why for F_{21} the unit vector is written as r_{12} instead of r_{21}?
     
  2. steveb

    Senior Member

    Jul 3, 2008
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    It simply eliminates the need for a negative sign in the formula. Since this is a vector equation, the equation must give the correct direction for the force vector. This means a negative sign is needed. But swapping the indices from 21 to 12 is the same as a negative sign.
     
  3. logearav

    Thread Starter Member

    Aug 19, 2011
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    Thanks for the reply steveb. Now look at this attachment. This material uses r_{21} for F_{21} which contradicts my previous attachment. Thats why i am confused.
     
  4. steveb

    Senior Member

    Jul 3, 2008
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    Yeah, these things are always confusing. You always have to carefully look at how the author is defining everything.

    As far as I can tell, each of your sources (EDIT: I mean attachements in this thread, not electric charges) uses a different definition for r21 and r12.

    The first document is much more clear about the definitions, while the second one does not clearly define everything. However, the second reference is probably using one of the accepted conventions that r21 is equal to r2-r1, where r2 and r1 are the position vectors of the charges, using an arbitrary reference frame.
     
    Last edited: Jan 4, 2012
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  5. studiot

    AAC Fanatic!

    Nov 9, 2007
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    Remember this is vector subtraction!
     
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  6. logearav

    Thread Starter Member

    Aug 19, 2011
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    So r12 is r1 - r2? Am i right?
     
  7. studiot

    AAC Fanatic!

    Nov 9, 2007
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    I was not querying your statement, just reminding folks that r1 and r2 are vectors so the statement r1-r2 or r2-r1 is a vector subtraction.
     
  8. logearav

    Thread Starter Member

    Aug 19, 2011
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    Now if the charges are opposite, will the force given by coulomb's law be negative, say
    F= -kQ1Q2/r^2?
    on simplifying will we get F = -9X10^9 Newton, if we take Q1 = 1C and Q2 as -1C and distance between them as 1 metre?
     
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