A wire, carrying a current `i`, is kept in the `x-y` plane along the curve `y = A sin ((2pi)/(lambda) x)`. A magnetic field `B` exista in the z-direction. Find the magnitude of the magnetic force on the portion of the wire between `x = 0 and x = lambda`.

Explanation

(a)
The magnetic force on wire `①` is equal and opposite to force on wire`②`
Semi-circular wire

Force on wire `① = 0`
Force on wire `② = Bi . 2R = 2 B i R`, upward
Hence net force on wire `= 2 B i R`, upward
OR
If a wire is other than straight wire, make it straight by joining initial and final end of wire. This straight length is the effective length.
(b)
`F = Bi.2R = 2 B i R`