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Electric Field due to line charge

  1. Mar 17, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    A non-conducting rod AB, having uniformly distributed positive charge of linear charge density λ is kept in x-y plane. The rod AB is inclined at an angle 30° with +ve Y-axis. The magnitude of electrostatic field at origin due to rod AB is E_0 N/C and its direction is along line OC. If line OC makes an angle θ=10a+b degree with negative x-axis as shown in the figure, calculate the value of (a+b) [OA=2m and λ=10^3 C/m]


    2. Relevant equations
    Please see the attached diagram

    3. The attempt at a solution

    [itex]E_x = \dfrac{\lambda}{4 \pi \epsilon _0 d} (\sin 60 + \sin 30) \\
    E_y = \dfrac{\lambda}{4 \pi \epsilon _0 d} |\cos 30 - \cos 60| \\

    \tan \alpha = \dfrac{E_y}{E_x} \\
    =\dfrac{ |\cos 30 - \cos 60| }{(\sin 60 + \sin 30)} [/itex]

    which comes out to be 15°.

    Thus, θ = 30° - 15° = 15°. So, a+b = 6. But it's not the correct answer :(
     

    Attached Files:

  2. jcsd
  3. Mar 19, 2014 #2
    I had a different result for ##E_y## but the same result for ##E_x##. How did you arrive at your expressions of the field components? I integrated over the line.
     
  4. Mar 20, 2014 #3

    utkarshakash

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    I did the integration again and got the expression for E_y as
    [itex] \dfrac{\lambda}{16 \pi \epsilon _0 d} (\cos 60^0 - \cos 120^0) [/itex]

    Do you get the same result?
     
  5. Jul 3, 2014 #4
    Hi utkarshakash

    1. Is θ=10a+b degree given and value of a+b is to be determined ?
    2. What are a and b ?
    3. What is the answer according to the key ?

    Thanks
     
    Last edited: Jul 3, 2014
  6. Jul 4, 2014 #5

    utkarshakash

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    1. Yes
    2. a and b are variables which need to be determined.
    3. I don't remember. I posted this a long time ago. I don't have the answer keys right now.
     
  7. Jul 4, 2014 #6
    Thank you :)

    But I wonder how is this possible . Value of θ can be determined which gives value of (10a+b) ,but then we need another equation in a and b to determine value of (a+b)

    Any thoughts ?
     
  8. Jul 4, 2014 #7

    utkarshakash

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    This is an integer type question. This means you'll have to get a and b by trial and error and I don't think it'd be difficult to do so.
     
  9. Jul 4, 2014 #8
    Fine . So a and b are integers . This is what I wanted to know .

    Thanks a lot :)
     
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