A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field B as shown in the figure. Determine the magnetic force on the wire if it carries a current i .

Step-by-step solution

The magnetic force on a current-carrying wire in a uniform magnetic field is given by F = i( L _ eff B ) , where L _ eff is the displacement vector from the initial point to the final point of the wire in the magnetic field. The wire consists of two vertical straight sections and a semicircular section. The straight sections carry current in opposite directions (one upwards, one downwards). The magnetic forces on these straight sections are equal in magnitude and opposite in direction (pointing horizontally outward