It may have occurred to you that since parallel currents attract, the current within a single wire should contract into a tiny concentrated stream along the axis. Yet in practice the current typically distributes itself quite uniformly over the wire. How do you account for this? If the positive charges (density ρ+) are "nailed down," and the negative charges (density ρ−) move at speed v (and none of these depends on the distance from the axis), show that ρ−=−ρ+γ2, where γ≡1/1−(v/c)2 and c2=1/μ0ϵ0. If the wire as a whole is neutral, where is the compensating charge located? [Notice that for typical velocities (see Prob. 5.20), the two charge densities are essentially unchanged by the current (since γ≈1). In plasmas, however, where the positive charges are also free to move, this so-called pinch effect can be very significant.]