E field outside a current carrying wire

[conquerer7]

Homework Statement

One step in one of the problems in my book (involving calculation of the Poynting vector) asks to find the electric field outside a wire. This wire is resistanceless and the current is steady.

Homework Equations

Maxwell's.

The Attempt at a Solution

Stared at it for a while, had no idea how there would possibly be an electric field, solutions manual says the wire creates a radial one proportional to 1/r.

 

[Mindscrape]

Hmm. This is a strange question. It seems your book is claiming that there is some linear charge density produced by the current, which then that makes a 1/r radial field. However, the linear charge density assumes a static scenario, which you don't have. Really, the way a wire works is that there is some potential across it V=IR, and the field is the gradient of the voltage (or, alternatively, the field is J/resistivity where J is current density).

 

[conquerer7]

Would this have anything to do with special relativity? I remember seeing something about length contraction when switching reference frames once, and about how that produced a charge density out of nowhere.

Edit: what if there's a nonzero resistance?

 

[tiny-tim]

which book?

 

[conquerer7]

5th edition of HRK's Physics, chapter 38, problem 11.

 

[tiny-tim]

i can only find the 6th edition online, http://books.google.co.uk/books?id=...ndamentals+of+Physics+"poynting+vector"&hl=en

can you find the equivalent passage there?