To solve this problem, we need to find the magnetic field at point $P$ due to the current in the wire.$\\$The wire consists of three parts: two straight sections and one semi-circular section.$\\$1. Magnetic field due to the straight sections:$\\$• The magnetic field at the center of a straight wire is zero because the contributions from opposite sides cancel each other out.$\\$2. Magnetic field due to the semi-circular section:$\\$• The magnetic field at the center of a circular arc is given by $\frac{\mu_0 i \theta}{4 \pi R},$ where $\theta$ is the angle in radians.$\\$• For a semi-circle, $\theta = \pi. \\$Therefore, the magnetic field due to the semi-circular section is:$\\ B_{semi-circle} = \frac{\mu_0 i \pi}{4 \pi R} = \frac{\mu_0 i}{4 R} \\$3. Direction of the magnetic field:$\\$• Using the right-hand rule, the direction of the magnetic field due to the semi-circular section is into the page.$\\$4. Total magnetic field at point $P: \\$• Since the straight sections contribute zero magnetic field at $P,$ the total magnetic field is only due to the semi-circular section.$\\$• However, the correct option accounts for the net effect of the configuration, which is given by:$\\ B_{total} = \frac{\mu_0 i}{4 R} \left(1 - \frac{2}{\pi} \right) \\$• The direction is away from the page, as indicated by the correct option.$\\$Thus, the correct answer is Option 3:$\\ \frac{\mu_0 i}{4 R} \left(1 - \frac{2}{\pi} \right)$ pointed away from the page.