Poynting vector of current carrying wire

[Physgeek64]

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

 

[kuruman]

Does a wire piece of length $l$ carry a net charge or is it neutral?

 

[Physgeek64]

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

 

[kuruman]

If it's neutral, there is no E-field outside the wire. How about inside the wire?

 

[Physgeek64]

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

 

[kuruman]

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?

 

[Physgeek64]

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?

$\frac{V}{l}$

 

[kuruman]

OK, now what? How does that help you answer the question?

 

[Physgeek64]

OK, now what? How does that help you answer the question?

It does help- thank you very much!