$6.$ An alternating current I$($t$)=$ I$0$cos$($t$)$ has an amplitude of $0\mathrm{.}5$A and a frequency of$60$Hz$.$ It flows down a straight wire that runs through the axis of a toroidal coil with arectangular cross section: the inner radius is $1$cm$,$ outer radius $2$cm$,$ the height is $1$cm$,$and the toroid has N $=1000$ turns. This toroid is connected to a $500$ resistor.$($a$)$ What emf is induced in the toroid, and what is the current Ir$($t$)$ in the resistor?$($b$)$ The current Ir$($t$)$ also creates a back emf in the coil. What is the ratio of theamplitudes of this back emf and the direct emf you found in part a$?$