The figure shows top view of a conducting rod AB, bent to form a semicircle of radius R, carrying current I, placed on a smooth horizontal table. It is subjected to a uniform magnetic field B perpendicular to its plane as shown. The rod is held at rest in its position by two light strings attached to its ends. Calculate the magnetic force acting on the conductor AB and the tension in the strings.
Strategy: To find the force conductor, consider a small arc of length `dl = Rd theta`. This arc can be consider as a straight conductor of length dl.

Explanation

Tension in the strings balances the magnetic force acting on the rod AB.
Magnetic force on AB is `Bixx` (effective length )`=Bi 2R`
Thus `2T=Bi2R`
`T=BiR`