• Support PF! Buy your school textbooks, materials and every day products Here!

Poynting vector of current carrying wire

  • Thread starter Physgeek64
  • Start date
  • #1
247
11

Homework Statement


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


Homework Equations




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
 

Answers and Replies

  • #2
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
9,049
2,442
Does a wire piece of length ##l## carry a net charge or is it neutral?
 
  • #3
247
11
Does a wire piece of length ##l## carry a net charge or is it neutral?
It is neutral. However I know there needs to be a poynting vector so I don't know how this works
 
  • #4
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
9,049
2,442
If it's neutral, there is no E-field outside the wire. How about inside the wire?
 
  • #5
247
11
If it's neutral, there is no E-field outside the wire. How about inside the wire?
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
 
  • #6
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
9,049
2,442
Not sure how to calculate its magnitude though
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?
 
  • #7
247
11
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?
##\frac{V}{l}##
 
  • #8
kuruman
Science Advisor
Homework Helper
Insights Author
Gold Member
9,049
2,442
OK, now what? How does that help you answer the question?
 
  • #9
247
11
OK, now what? How does that help you answer the question?
It does help- thank you very much!!
 

Related Threads on Poynting vector of current carrying wire

  • Last Post
Replies
3
Views
14K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
4K
Replies
6
Views
6K
  • Last Post
Replies
12
Views
2K
Replies
5
Views
12K
Top