A rectangular coil in the plane of the page has dimensions a and b. A long wire that carries a current I is placed directly on the coil, as shown in Fig. 13.20. (i) Obtain an expression for the magnetic flux through the coil as a function of x for 0 <= x <= b. (ii) For what value of x is the net flux through the coil a maximum? For what value of x is the net flux a minimum? (iii) Obtain an expression for the emf induced in the coil if the wire is placed at x = b/4 and the current varies with time according to I = 2t .