A toroid has a core (non-ferromagnetic) of inner radius 23 cm and outer radius 28 cm, around which 4000 turns of a wire are wound. If the current in the wire is 9 A, find the magnetic field (a) inside the core of the toroid (b) outside the toroid?

Correct option is A

​$$\text{Given:} \\\text{Inner radius of toroid, } r_2 = 23 \, \text{cm} = 0.23 \, \text{m} \\\text{Outer radius of toroid, } r_1 = 28 \, \text{cm} = 0.28 \, \text{m} \\\text{Number of turns, } N = 4000 \\\text{Current, } I = 9 \, \text{A} \\\text{Case (a) Inside the core of the toroid:} \\\text{The magnetic field inside the toroid is given by the formula:} \\B = \dfrac{\mu_0 N I}{L} \\\text{Where:} \\L \text{ is the average length of the toroid's circular path, which is the mean radius:} \\L = \pi \left( \dfrac{r_1 + r_2}{2} \right) \\L = \pi \left( \dfrac{0.28 + 0.23}{2} \right) = 0.51 \pi \\\text{Now, using the formula for magnetic field:} \\B = \dfrac{4\pi \times 10^{-7} \times 4000 \times 9}{0.51 \pi} \\B = 2.82 \times 10^{-2} \, \text{T}$$

$$\text{Case (b) Outside the toroid:} \\\text{The magnetic field outside the toroid is zero because the magnetic field lines do not extend outside a toroid.} \\\text{This is due to the closed nature of the current path and the lack of a net current outside.} \\\text{Therefore:} \\B = 0 \, \text{T}$$​​​