# Poynting vector of current carrying wire

## 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

## 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

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kuruman
Homework Helper
Gold Member
Does a wire piece of length ##l## carry a net charge or is it neutral?

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

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
Homework Helper
Gold Member
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?

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