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$(25)1.$ Rail guns have been touted as kinetic weapons of the futurel There are some pros and cons to them that your lab group may investigate in preparation for your Lab $10$ presentation. One of the drawbacks is that current flows along the rails and crosses over between the rails through the armature $($shown below in black$).$ The rails generate a magnetic field that propels the armature down the rails and out the end of the "barrel". The armature discards via drag forces fully exposing the projectile $($shown below in green$),$ which travels at a hypersonic velocity. Unfortunately, the force on the current carrying armature is not the only physics at play. Faraday's Law plays a part.

System specifications: the current provided by the power supply is $6\mathrm{.}00{10}^6$Amps; the total mass of the projectile and armature system is $5\mathrm{.}00$ kilograms; the rails are $L=10\mathrm{.}0m$ long and $b=0\mathrm{.}300m$ apart; and the total resistance of the system is $R=10\mathrm{.}0.$ Assumptions: the current provided by the power supply is constant, assume no friction $($air or rails$),$ you can treat the current moving through the rails as if they were "long straight wires". A$)$ Calculate the current induced from the armature moving along the rails at the time when the armature reaches the end of the barrel. B$)$ Calculate the armature's velocity at the end of the barrel. C$)$ Comment on what impact the induced current has on the rail gun system.

b