A conducting sliding bar oscillates over two parallel conduct$-$

ing rals in a sinusoidally varying magnetic field

B$=$hat$($z$)5$cos$\backslash$omega t

as shown in the figure. The position of the sliding bar is given by x$=$

$0\mathrm{.}35(1-$cos$\backslash$omega t$)$ and the rails are terminated in a resistance R$=0\mathrm{.}2\backslash$Omega $.$

Find the current i$.$

Please solve by integrating over the area