A very thin wire, which follows a semicircular curve C of radius R, lies in the upper half of the x-y plane with its center at the origin. There is a constant current I flowing counter clockwise, starting upward from the end of the wire on the positive x axis and ending downward at the end on the negative x axis. The wire is in a uniform magnetic field, which has magnitude Bo and direction parallel to the z axis in the positive z direction. Determine a symbolic answer in unit-vector notation for the total force on the wire due to the magnetic field. Ignore the forces on the leads that carry the current into the wire at the right end and out of the wire at the left end.
(Solution check: The numerical value with I = 2.00 A, Bo = 3.00 T, and R = 4.00 m is 48.0 N.)