Analternating current I$($t$)=$ I$0$ cos$($t$)($amplitude $0\mathrm{.}5$ A$,$ frequency $60$ Hz$)$ flows down a straight wire, which runs along the axis of a toroidal coil with rectangular cross section $($inner radius $1$ cm$,$ outer radius $2$ cm$,$ height $1$ cm$,1000$ turns$).$ The coil is connected to a $500$ resistor. $($a$)$ In the quasistatic approximation, what emf is induced in the toroid? Find the current, IR$($t$),$ in the resistor. $($b$)$ Calculate the back emf in the coil, due to the current IR$($t$).$ What is the ratio of the amplitudes of this back emf and the $$direct$$ emf in $($a$)?$