field outside its cross$-$sectional area. The current in the solenoid is increasing at a rate of $\frac{\text{I}}{}t.$

Figure P$31\mathrm{.}7$

$($a$)$ What is the induced current in the ring? $($Use any variable or symbol stated above along with the following as necessary: ${}_0$ and ${}_0)$

$I_{\text{r}\text{i}\text{n}\text{g}}=\frac{\text{I}}{}t$

$($b$)$ At the center of the ring, what is the magnetic field produced by the induced current in the ring? $($Use any variable or symbol stated above along with the following as necessary: ${}_0$ and $.$ Do not use $I_{\text{r}\text{i}\text{n}\text{g}}$ in your answer.$)$

$B=\frac{\text{I}}{}t$

$($c$)$ What is the direction of this field?

$B_{\text{r}\text{i}\text{n}\text{g}}$ points downward.

$B_{\text{r}\text{i}\text{n}\text{g}}$ points upward.