A loop of wire in the shape of a rectangle of width $w$ and length $L$ and a long, straight wire carrying a current $I$ lie on a tabletop as shown in Figure P31.11. (a) Determine the magnetic flux through the loop due to the current $I$ (b) Suppose the current is changing with time according to $I=a+b t,$ where $a$ and $b$ are constants. Determine the emf that is induced in the loop if $b=10.0 \mathrm{A} / \mathrm{s}, h=1.00 \mathrm{cm},$ $w=10.0 \mathrm{cm},$ and $L=1.00 \mathrm{m} .$ (c) What is the direction of the induced current in the rectangle?