The potential energy and electric field?

What is the energy density of the ELECTRIC field for a wire that is 10mm in diameter and carrying 10A?

• Is it zero? I think this is trick question. Does a current carrying wire induce an electric field as well as a magnetic field. I calculated the energy density of the magnetic field but the next question asked for the energy density of the electric field.

• Answer:

  I'm assuming that the current is not changing with time other than the initial turn-on transient. When the current has reached a steady state (didn't say reached zero, but some final state), you are in the area of electromagnetics called electro/magnetostatics and the magnetic and electric fields are uncoupled. For the situation that you describe (I'm assuming no stationary charges external to the wire), the Electric Field Density is zero. You might be tempted to use Gauss' Law to find the Electric Field from an individual electron as it moved down the wire, but the summation at any particular point in space from all charges moving in the wire will sum to zero. When the current is first turned on you will have a changing magnetic field and therefore an electric field. However, that electric field will die away rapidly.