A rod of mass `m` and resistnce `R` sldes on frictionless and resistanceless rails a distance `l` a part thast innclude a source of emf `E_0` (see figure). The rod is initially at rest. Find the expression for the
a. Velocity of the rod v(t). b. current in the loop i(t).

Answer

B

Explanation

a. Let at time velocity of rod be `v` (towards right) and current in the cirucit is `i` (from `a` to `b`). The magnetic force on is `ilB` (towards right).
Writing the equation of motion of the rod
`m.(dv)/(dt)=ilB=((E_0-Blv)/R)lB`
`int_0^v (dv)/((E_(0)Bl)/(mR)-(B^(2)l^(2))/(mR)v)= int_(0)^(t) dt`
`:. v=E_0/(Bl)(1-e^(-(B^2i^2)/(mR)t))`
b. `i=(E_0-Blv)/R`