Prob. $9(10$ pts$)$ A conducting sliding bar oscillates over two parallel conducting rails in a sinusoidally varying magnetic field

$B=$hat$(z)5cost$

as shown in the figure. The position of the sliding bar is given by $x=0\mathrm{.}35(1-cost)$ and the rails are terminated in a resistance $R=0\mathrm{.}2.$ Find the current $i.$