How Do You Calculate Electric Energy Density Near a Copper Wire?

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Homework Statement

Calculate the electric energy density at the surface of a 3.4 mm diameter copper wire carrying a 28 A current.

Homework Equations

u = (1/2) ε₀ E²

The Attempt at a Solution

With the electric energy density equation, I substituted in the equation for the electric field for an infinite line charge:

u = (1/2) ε₀ ( λ/ (ε₀ 2 π r ))²

I have all the information except for the charge density, λ. I know that it's a copper wire, but how can I find what λ is with that information?

 

[TSny]

I think that you are supposed to assume that the electric field at the surface of the wire is the same as the electric field inside the wire. The electric field inside the wire pushes the electrons through the copper.

Can you determine E inside the wire from the current, the diameter of the wire, and the properties of copper?