# Metal bar on rails, induced emf

A metal bar with length L, mass m, and resistance R is placed on frictionless metal rails that
are inclined at an angle α above the horizontal. The top end of the rails are connected with a
conducting wire. The resistance of the rails and wire are negligible. The rails are embedded in a
uniform magnetic field B perpendicular to the plane in which the rails sit. The bar is released from
rest and slides down the rails. Determine the magnitude of the induced emf on the loop after a generic time τ , shorter than the time required to reach the terminal velocity.

I know that $|\epsilon|=\frac{d\phi}{dt}$, where in this case $d\phi=BdA=BL\frac{g}{2}sin(\alpha)\tau^{2}$ and $dt=\tau$, so $|\epsilon|=BL\frac{g}{2}sin(\alpha)\tau$. But it doesn’t seem right to me because at some point, the bar will reach terminal velocity, which means the bar must be decelerating and I haven’t taken that into account because I don’t know how to. Any help will be appreciated.

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