A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in time according to B Bmaxe t$/$t$,$ where Bmax and t are constants. The field has the constant value Bmax for t $0.($a$)$ Use Faraday$$s law to show that the emf induced in the loop is given by $($b$)$ Obtain a numerical value for e at t $4\mathrm{.}00$ s when A $0\mathrm{.}160$ m$2,$ Bmax $0\mathrm{.}350$ T$,$ and t $2\mathrm{.}00$ s$.($c$)$ For the values of A$,$ Bmax, and t given in part $($b$),$ what is the maximum value of e$?$