Q: A horizontal straight conductor of mass m and length l is placed in a uniform magnetic field of magnitude B. An amount of charge Q passes through the rod in a very short time such that the conductor begins to move only after all the charge has passage through it. Its initial velocity will be
(a) B Q l m
(b) (B Q l )/m
(c) (B Q )/(l m)
(d) (B l )/(m Q)
Ans: (b)
Sol : If I is the current passing through the rod, then magnetic force on the rod is
F = Bi l
The impulse given by this force to the rod,
$ \displaystyle J = \int F dt $
$ \displaystyle J = \int B l (i dt ) = B l Q $ …(i)
If u is initial velocity acquired by the rod, then
Impulse J = mu …(ii)
From (i) and (ii),
mu = BlQ
u = BlQ/m