A straight, current-carrying wire is positioned along the axis of a...

Let the straight current-carrying wire be placed along the z-axis. The magnetic field produced by this wire at a distance $r$ is given by $\vec{B} = \dfrac{\mu_0 I}{2\pi r} \hat{\phi}$, which is tangential to any circle centered on the axis.

The circular loop is centered on the axis, so its current elements $d\vec{l}$ are also directed along the tangential direction ($\hat{\phi}$).

The magnetic force on a small current element of the loop is given by $d\vec{F} = I (d\vec{l} \times \vec{B})$.

Since both the current element $d\vec{l}$ and the magnetic field $\vec{B}$ are along the same line (parallel or anti-parallel), the cross product $d\vec{l} \times \vec{B}$ is zero.

Therefore, the straight wire exerts zero magnetic force on the circular loop.