$A$ toroid has a core (non-ferromagnetic) of inner radius $25 \; cm$ and outer radius $26 \; cm,$ around which $3500$ turns of a wire are wound. If the current in the wire is $11 \; A$,what is the magnetic field:
$(a)$ outside the toroid,
$(b)$ inside the core of the toroid,and
$(c)$ in the empty space surrounded by the toroid?

(B) Given:
Inner radius $r_{1} = 25 \; cm = 0.25 \; m$
Outer radius $r_{2} = 26 \; cm = 0.26 \; m$
Number of turns $N = 3500$
Current $I = 11 \; A$
$(a)$ The magnetic field outside a toroid is zero because the net current enclosed by an Amperian loop outside the toroid is zero.
$(b)$ The magnetic field inside the core of a toroid is given by $B = \frac{\mu_{0} N I}{l}$,where $l$ is the mean circumference.
Mean radius $r = \frac{r_{1} + r_{2}}{2} = \frac{0.25 + 0.26}{2} = 0.255 \; m$
Mean length $l = 2 \pi r = 2 \pi (0.255) = 0.51 \pi \; m$
Using $\mu_{0} = 4 \pi \times 10^{-7} \; T \cdot m \cdot A^{-1}$:
$B = \frac{4 \pi \times 10^{-7} \times 3500 \times 11}{0.51 \pi} = \frac{4 \times 10^{-7} \times 38500}{0.51} \approx 3.02 \times 10^{-2} \; T$
$(c)$ The magnetic field in the empty space surrounded by the toroid is zero,as the net current enclosed by an Amperian loop in this region is zero.