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Two oppositely charged wires and their capacitance

  1. Apr 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Two long wires with the same cross section are arranged in air PARALLEL to each other . Assume both have opposite charge densities +λ and -λ. The distance between the axis of the wire is η times larger than the radius(r) of wires cross section . What would be the capacitance of the wires per unit lenth?

    2. Relevant equations
    Electric field of any point between these wires at a distance x from the +λ charged wire is
    λ/2πε[1/(x)+1/(ηr-x)]

    3. The attempt at a solution
    The problem I am facing is about the limits to be used while integrating Electric field to get the potential .
    We know that V=-∫Edx
    (Between some limits)
    So ∫Edx =λ/2πε[ln(x/ηr-x)]
    And if I integrate it over 0 to ηr
    The I will get stuff like ln 0 and ln∞ which are obviously not defined . Some other limits just dont get the right answer which is πε/ ln η .
     
  2. jcsd
  3. Apr 14, 2015 #2
    1) 'x' gives distance between which two points ?
    2) What is the initial point ?
    3) Now answer ,what should be the lower limit in the integration ?
     
  4. Apr 14, 2015 #3
    O-----------O
    <----->is x
    Initial point is the centre of the first+λ charged wire (I think).
    So what I think is that the lower limit should be 0 and the upper limit should be ηr. BUT , when I put them in the integrated electric field the answer is absurd.....
     
  5. Apr 14, 2015 #4
    Right .

    But , does electric field exist within the wire ? The electric field does work from the surface of wire +λ to the closest point on the surface of other wire -λ.
     
  6. Apr 14, 2015 #5
    No. There is no electric field inside the wires .... therefore I should take the limits from r to ηr-r.
    After doing the calculation I found that the potential is
    V=λ/πε[ln(η-1)]
    Since we're talking about a unit length thus λ=Q
    So Capacitance=C=Q/V=πε/ln(η-1)
    Which is just a little different from the answer(which now seems incorrect to me) So am I right here????
    Edit: hey !hey!hey! In the question its given that η>>1 thus η-1≈η so now I got the correct answer ....now I am happy..... thank you for your guidance dd.!!!!
     
    Last edited: Apr 14, 2015
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