Poynting vector of current carrying wire

In summary, the conversation discussed finding the Poynting vector of a wire with constant current, as well as the direction of the electric and magnetic fields. It also touched on the concept of a neutral wire and calculating the magnitude of the E-field inside the wire. Through the discussion, it was determined that the potential difference across the ends of the wire can help calculate the E-field inside the wire.
  • #1
Physgeek64
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
 
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  • #2
Does a wire piece of length ##l## carry a net charge or is it neutral?
 
  • #3
kuruman said:
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
If it's neutral, there is no E-field outside the wire. How about inside the wire?
 
  • #5
kuruman said:
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
Physgeek64 said:
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
kuruman said:
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
OK, now what? How does that help you answer the question?
 
  • #9
kuruman said:
OK, now what? How does that help you answer the question?
It does help- thank you very much!
 

What is the Poynting vector of a current carrying wire?

The Poynting vector of a current carrying wire is a mathematical quantity that describes the flow of electromagnetic energy in the form of electromagnetic waves. It is a vector quantity that has both magnitude and direction.

How is the Poynting vector calculated for a current carrying wire?

The Poynting vector for a current carrying wire can be calculated by taking the cross product of the electric field and magnetic field vectors at a given point in space. It is given by the equation S = E x H, where S is the Poynting vector, E is the electric field, and H is the magnetic field.

What does the direction of the Poynting vector indicate?

The direction of the Poynting vector indicates the direction of energy flow. It points in the direction of propagation of electromagnetic waves and is perpendicular to both the electric and magnetic fields.

What is the significance of the Poynting vector for a current carrying wire?

The Poynting vector is significant for a current carrying wire because it helps us understand how electromagnetic energy is transferred from one point to another. It also plays a crucial role in the study of electromagnetic radiation and its effects on the surrounding environment.

How does the Poynting vector change with respect to the current and wire properties?

The magnitude of the Poynting vector is directly proportional to the square of the current and is affected by the properties of the wire such as its conductivity and dimensions. As the current or wire properties change, the magnitude and direction of the Poynting vector also change accordingly.

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