I'd rather have just commented, but since I got an account here just because of this, I will attempt an answer, but cannot help but try to redirect some of the commentary here.
Simple answer: Yes, in an ideal case. If you construct the model you will see that that current density shrinks to zero at the centerline of the conductor, where E vector is zero. This takes some work beyond the statement of Maxwell's Equations.
Reality is of course not so cut and dried. But the gradient of current density is still very significant. Do you want to know why Nikolai Tesla could deomonstrate the phenonemon using his own body? Well, here you have it.
So, use stranded wire for speaker cables, ipod jacks, etc. It's total current capacity (due to heat) is lower, so don't wire your house with it.
Finally, the separation of power transmission lines is to reduce losses due to capacitive coupling. But while we're on the subject, check out Hoover Dam. There you can buy a section of the original tranmission line from the dam to the grid. It's copper, made of interlocking radial cross-section parts. And yes, it's hollow. For 60Hz.
There you go.
And to the other commentor, yes this darn well ought to be the selected answer. But heck, what do I know, zero points and all.
Martin: I lost track of how many incorrect statements you made. I have been a programmer too, but I am also an EE. Your romper-room grade commentary should not go unanswered. I would say the same thing to whomever allegedly moderates this forum. The lot of you ought to know better.
To abatter: Please try to understand the concept of current density in a conductor.
I CAN'T BELIEVE THIS IS A PHYSICS FORUM