Induced emf of Sliding Wire Down Rails

[Blitzmeister]

Homework Statement

[This is the best image I could find]

The link on the bottom part of the rails is now removed creating two parallel wires that are not connected (so no longer U shaped but just two rails).
Now a wire of length L, mass m and resistance R slides without friction down parallel conducting rails of negligible resistance. The rails make an angle of θ with the horizontal and a uniform magnetic field B points vertically upward throughout the region. If the wire starts from rest, what emf will be observed across it after it travels 0.05m?

Homework Equations

I don't know if any that I know apply

The Attempt at a Solution

So if the bottom part of the rails were there, I would just need to apply Faraday's Law and be done: (e.g. ε = -dΦ_B/dt; Φ_B = B dot A ∴ ε = BLvcosθ, then to solve for v we just set force of gravity equal to magnetic force and substitute back into original equation)
However, the bottom part of the rails is not there, and I don't know how to start. I would make a guess and say ε = 0 since there is no loop

 

[BvU]

Hello BM, and welcome to PF !

Not much to go on then, eh ? No equations and no bottom part, so the whole attempt at solution goes down the drain !

Homework Equations

[/B]
I don't know if any that I know apply

Let me try to verify that: ever heard of the Lorentz force ? If yes, then you do know one that applies !

In the moving wire, there are free charge carriers and they too are moving through a magnetic field. So they will go where the Lorentz force forces them !
And they can't go far if the loop isn't closed, right ? Because when they are pushed together one way, they build up an electric field in the conductor. Stops them from moving (because the Lorentz force is now zero), But that E field constitutes a potential difference, an emf ! Just like in Faraday's law. And you already know what to do when that applies! Isn't that cute ?

Check out the link between Lorentz force and Faradady's law here.