As shown in the figure, a strong electromagnet produces a magnetic...

Given parameters are magnetic field $B = 1.0 \text{ T}$, radius of the cylindrical region $r = 4.0 \text{ cm} = 0.04 \text{ m}$, and current $i = 2.0 \text{ A}$.

Since the wire intersects the axis of the cylindrical region, the length of the wire inside the magnetic field is equal to the diameter of the cylinder.

Effective length of the wire in the magnetic field is $l = 2r = 2 \times 0.04 = 0.08 \text{ m}$.

The magnetic force on the current-carrying wire is given by $F = i l B \sin\theta$.

As the wire is perpendicular to the magnetic field, $\theta = 90^{\circ}$.

Substituting the values, we get:

$F = 2.0 \times 0.08 \times 1.0 \times \sin 90^{\circ}$

$F = 0.16 \text{ N}$