For wires bent into complex shapes: (1) Break into simple segments (straight lines, arcs). (2) Calculate $\vec{B}$ from each segment independently. (3) Add vectorially. Key shortcuts: straight wire through the point contributes zero. A complete loop of radius $R$ contributes $\mu_0 I/(2R)$. A fraction $\theta/(2\pi)$ of a loop contributes $\mu_0 I\theta/(4\pi R)$. Two coplanar semicircles of different radii with common center: fields add or subtract depending on current direction.