The mutual inductance between two coils is M$=1$ mH$.$ Coil $1,$ made up of $100$ turns, has an inductance L$1=25$ mH$.$ Coil $2,$ made up of $200$ turns, has an inductance L$2=25$ mH$.$ At t$=0,7$ mA current flows through coil $1$ and is changing at a rate of $2$ A$/$s$.$ Part $($a$)$ What is the magnetic flux $\backslash$Phi $1$ through coil $1$ at t$=0?$ Part $($b$)$ What is the magnitude of the self induced emf generated in coil $1?$ Part $($c$)$ What is the magnetic flux $\backslash$Phi $21$ through coil $2$ at t$=0?$ Part $($d$)$ What is the magnitude of the mutually induced emf that appears in coil $2?$