$9.$ The figure shows two concentric coils. The outer coil has a diameter of $\backslash (1\mathrm{.}1\backslash$mathrm$\{$~cm$\},100\backslash )$ turns, a length of $10$ cm and the current goes from $0$ to $5$ A in $10$ ms $.$ The inner coil has a diameter of $1$ cm is $30$ cm long.

$($a$)(1$ point$)$ You want the inner coil to have an emf of $1$ volt. How many turns should it have to generate this emf?

$($b$)(1$ point$)$ The current direction is shown in the outer coil, what will the direction of the induced current be in the inner coil?