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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 $\frac{F}{L}=\frac{\int_{0}^{\pi}2\mu_0dI(\theta)^2}{4\pi}$.

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Yes.

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

The magnetic field generated by the current carrying wire itself is used in the z-pinch experiments in plasma physics.

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  • $\begingroup$ Right, a pinch! How could I forget my Ocean's Eleven. Can you provide a more specific formula, or point me to a derivation, or even an exercise in Griffiths, that would allow a reasonable order of magnitude estimation of the force/pressure? F = J x B is way too general to be practical. $\endgroup$ – Moobie Nov 27 '19 at 22:56
  • $\begingroup$ You just integrate it with your particular J and B to get the total force... it depends on coil geometry $\endgroup$ – SuperCiocia Nov 28 '19 at 13:54

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