A toroid is made of 2 000 turns of wire of radius 2.00 cm formed into a donut shape of inner radius 10.0 cm and outer radius 14.0 cm. When a 30.0-A current is present in the toroid, the magnetic field at a distance of 11.0 cm from the center of the toroid is
A) 0.0857 T.
B) 0.109 T.
C) 0.120 T.
D) 0.600 T.
E) 0.685 T.

Question

Quizplus · Accepted Answer

The magnetic field inside a toroid at a distance $r$ from the center is given by $B = \frac{\mu_0 N I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}$, $N$ is the number of turns, and $I$ is the current. Given $N = 2000$, $I = 30.0 \, \text{A}$, and $r = 11.0 \, \text{cm} = 0.11 \, \text{m}$, we can calculate $B$:$$B = \frac{(4\pi \times 10^{-7}) \times 2000 \times 30.0}{2\pi \times 0.11} = \frac{24 \times 10^{-4}}{0.22} = 0.109 \, \text{T}$$

A Toroid Is Made of 2 000 Turns of Wire