A toroid (solenoid bent into a ring) with $N$ total turns and mean radius $r$: inside the toroid $B = \mu_0 NI/(2\pi r)$. Outside (both inside the hole and outside the ring): $B = 0$. Unlike a solenoid, the field varies within the cross-section ($B \propto 1/r$). For a thin toroid ($R_{\text{inner}} \approx R_{\text{outer}}$), $B$ is approximately uniform. The field inside the empty space enclosed by the toroid is zero — this is a common trap.