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"Potential of Concentric Cylindrical Insulator and Conducting Shell"

  1. Aug 4, 2014 #1
    1. The problem statement, all variables and given/known data
    h6_cylinder.png
    An infinitely long solid insulating cylinder of radius a = 2.5 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 30 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 15.3 cm, and outer radius c = 19.3 cm. The conducting shell has a linear charge density λ = -0.32μC/m.d=51cm.

    What is V(c) - V(a), the potentital difference between the outer surface of the conductor and the outer surface of the insulator?

    2. Relevant equations

    ΔV=-∫E*dr.
    E=λ/2ε0

    3. The attempt at a solution

    ΔV=Vab+Vbc; Eab=λ/2ε0;
    Ebc I used flux EA=Qenc/ε0 → E=(Qenc)/2*∏*r*L*ε0 → Vbc=∫(b→c) (Qenc)/(2*∏*r*L*ε0 ) *dr
    This is basically how I did it, But I got the wrong answer -4397..Please help me ??
     
  2. jcsd
  3. Aug 4, 2014 #2

    Zondrina

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    What is the potential of the outer charge distribution? Take a differential charge element ##dq = \lambda ds## to find it.

    How about the inner one now? Take a differential charge element ##dq = \rho dV##.
     
  4. Aug 4, 2014 #3

    Hmmmm Sorry I am a little bit confused. What's differential charge element?? I guess haven't learnt that in math yet. I only know integral and derivatives.. Can you please explain it in a easier way? Thank you
     
  5. Aug 4, 2014 #4

    Zondrina

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    Wow sorry ignore my last post. I should have read your post more carefully.

    What did you compute for the electric field of the inner cylinder? Your formula looks wrong it should be:

    ##E = \frac{\lambda}{2 \pi \epsilon_0 r}##

    I was a bit thrown off by that random point (d,d) I saw in the image.
     
  6. Aug 4, 2014 #5
    hmmm sorry I can't remember. But I think the basic idea of my solution was wrong.. because I basically just made it up... Can you please let me know how would the correct solution be?(or just the basic idea and structure of it )
    Thank you!
     
  7. Aug 4, 2014 #6

    Zondrina

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    Find the electric field of the infinitely long line of charge at a radial distance ##r## away.

    Integrate this uniform field over the path length.
     
  8. Aug 4, 2014 #7
    Just the infinite line? So ignore the field by the shell? but the r starts from the outer surface of the shell though?
     
  9. Aug 4, 2014 #8

    Zondrina

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    No don't ignore the field of the shell.

    What is the electric field due to a charged ring?
     
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