Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

$$\vec{B}_{\text{net}} = \vec{B}_{\text{top\_wire}} + \vec{B}_{\text{semicircle}} + \vec{B}_{\text{bottom\_wire}}$$

$$B_{\text{bottom\_wire}} = 0 \quad (\text{point lies along its line of action})$$

$$B_{\text{top\_wire}} = \frac{\mu_0 i}{4\pi r} \quad (\text{directed out of the page, }\hat{k})$$

$$B_{\text{semicircle}} = \frac{1}{2}\left(\frac{\mu_0 i}{2r}\right) = \frac{\mu_0 i}{4r} \quad (\text{directed out of the page, }\hat{k})$$

$$B_{\text{net}} = \frac{\mu_0 i}{4r} + \frac{\mu_0 i}{4\pi r} = \frac{\mu_0 i}{2r}\left(\frac{1}{2} + \frac{1}{2\pi}\right)$$