In the following figure magnitude of the magnetic field at the point p is

Step-by-step solution

The magnetic field at point P is the vector sum of contributions from the three wire segments: vertical semi-infinite wire, semicircular arc, and horizontal semi-infinite wire, all with current I . The vertical semi-infinite wire at perpendicular distance r contributes B₁ = ₀ I 4 r into the page by the right-hand rule. The semicircular arc of radius r centered at P yields B₂ = ₀ I 4r into the page, as the field for a full circle is ₀ I 2r and halved for a semicircle. The horizontal semi-infinite wire analogously co