# Does Ampère's force law apply to a single wire?

In a typical example of Ampère's force law, it is shown that two current-carrying wires can magnetically attract each other (when the currents are in the same direction).

On a single conducting wire with finite radius, is there an inward force compressing the wire due to the same effect? (Yes. As pointed out in an answer, this is known as a pinch.)

What is the expression for the force and energy per unit length of this effect on a single infinite cylindrical wire, not subjected to external E/B-field?

Since normally the current travels along the skin of a wire, one may consider the surface of a wire as infinitely many tiny parallel wires. I can imagine that one may integrate over something like $$\frac{F}{L}=\frac{\int_{0}^{\pi}2\mu_0dI(\theta)^2}{4\pi}$$.

Usually in these cases you’d calculate the force volume density $$\mathcal{F}$$: $$\mathbf{\mathcal{F}} = \mathbf{J}\times \mathbf{B}.$$