Question

In figure, there are two sliders and they can slide on two frictionless parallel wires in uniform magnetic field $B$, which is present everywhere. The mass of each slider is $m$, resistance $R$ and initially these are at rest. Now, if one slider is given a velocity $v_0=16m{s}^{-1}$, what will be the velocity (in $m{s}^{-1}$) of other slider after long time? (neglect the self-induction)

Answer 1

After very long time, both the sliders have to be at the same velocity
so that

$E=\frac{d\varphi }{dt}=0$
Since the initial energy will be dissipated as heat

If $E=0$
both have the same velocity
Conservation of Momentum (frictionless, hence no external force)

$mv+mv=m{v}_o$
$v=\frac{v_o}{2}$

$v=8m/s$