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Homework Help: Poynting vector of current carrying wire

  1. Dec 30, 2017 #1
    1. The problem statement, all variables and given/known data
    A long straight wire of radius a and resistance per unit length R carries a constant current I. Find the Poynting vector N = E × H at the surface of the wire and give
    a sketch showing the directions of the current, the electric field E, the magnetic field
    H, and N. Integrate the Poynting vector over the surface of a length l of the wire and comment on your result


    2. Relevant equations


    3. The attempt at a solution
    ##\integral{H\dot dl}=I_{free}##
    ##H(2\pi r)=I##
    ##H|_a=\frac{I}{2\pi a} \hat{\theta}##

    E outside the wire will be ##E=-\frac{\lambda}{2\pi\epsilon r } \hat{r}##

    I don't know if this is the same as the E field at the surface? Also I don't know how to get ##\lambda## in terms of I and R

    then ##S=E\cross H ##

    Many thanks
     
  2. jcsd
  3. Dec 30, 2017 #2

    kuruman

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    Does a wire piece of length ##l## carry a net charge or is it neutral?
     
  4. Dec 30, 2017 #3
    It is neutral. However I know there needs to be a poynting vector so I don't know how this works
     
  5. Dec 30, 2017 #4

    kuruman

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    If it's neutral, there is no E-field outside the wire. How about inside the wire?
     
  6. Dec 31, 2017 #5
    Inside the wire we have a non-neutral charge. Negative electrons flow in one direction, leaving positive ions behind. Hence we have an E-field in the direction of current? Not sure how to calculate its magnitude though
     
  7. Dec 31, 2017 #6

    kuruman

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    You know that the potential difference across the two ends of the wire is V. If the distance between the ends is ##l##, what is E?
     
  8. Dec 31, 2017 #7
    ##\frac{V}{l}##
     
  9. Dec 31, 2017 #8

    kuruman

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    OK, now what? How does that help you answer the question?
     
  10. Dec 31, 2017 #9
    It does help- thank you very much!!
     
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