1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    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
    <----->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
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted