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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 $v_0=16ms^{−1}$ , what will be the velocity of other sliders after a long time?

I can't seem to figure this question out there are just way too many things happening at once

So starting off ,an motional emf will be developed across the first rod because of which there will be current in rod 2 as well which in turn will experience a magnetic force due to which it will start moving and generate another emf along with a new opposing current

How do i account for all these at once?

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The best way to do this would be by conserving energy,

initially, let the energy of the 1st slider be E,

we know that finally, the the velocity of the slider is constant, therefore the force acting is 0.

The only force that acts on the slider is the magnetic force due to the current flow. since the force is zero, current is also 0. Therefore, the volatge is 0.

this implies that the magnetic flux is constant between the two sliders. i.e they have equal velocities.

they have the same mass, therefore V1 = V2 = 1/2 (Vi) in this case, V=8

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