$2.(25$p$)$ A simple rotating loop between curved pole faces is connected to a battery and a resistor through a switch. The resistor $(")$ represents the total resistance of the battery and the wire in the machine. The specifications of this machine are $"=0\mathrm{.}3,,$$ $=120,,0=0\mathrm{.}252$ with loop dimensions of $,3=1\mathrm{.}04$ and $5=0\mathrm{.}54.($a$)$ Suppose a load is attached to the loop, and the resulting load torque is $10$ N$-$m$.$ What would the new steady$-$state speed be$?$ How much power is supplied to the shaft of the machine? How much power is being supplied by the battery? Is this machine a motor or a generator? $($b$)$ Suppose the machine is running unloaded. What would the final steady$-$state speed of the rotor be if the flux density were reduced to $0\mathrm{.}20$ T$?$