A constant current `i` flows through a metal rod of length `L` and mass `m` that slides on frictionless rails as shown in Fig. If the initial speed of the rod is `v_(0)` towards right and a magnetic field `B` acts vertically up, find (a) the speed of the rod as a function of time, (b) the total distance moved by the rod before coming to a stop.

Explanation

Force on rod: `F_(m) = BiL`, towards left
Retardation of rod `a = (F_(m))/(m) = (Bil)/(m)`
Retardation is constant
(a) `v = u - at`
`= v_(0) - (BiL)/(m)t`
(b) `v^(2) = u^(2) - 2 as`
`0 = v_(0)^(2) - (2BiL)/(m)s`
`s = (mv_(0)^(2))/(2 BiL)`