Question

a toroid is a solenoid in the shape of a donut (figure 1). figure 1 of 1 part d if not, how does it vary? $bpropto1/r$ $bpropto r$ $bpropto1/r^{2}$ $bpropto r^{2}$

Explanation:

Step1: Recall magnetic - field formula for toroid

The magnetic field inside a toroid is given by $B=\frac{\mu_0NI}{2\pi R}$, where $\mu_0$ is the permeability of free - space, $N$ is the total number of turns, $I$ is the current, and $R$ is the radius of the toroid.

Step2: Analyze the proportionality

From the formula $B=\frac{\mu_0NI}{2\pi R}$, we can see that $B\propto\frac{1}{R}$ when $\mu_0$, $N$, and $I$ are constant.

Answer:

$B\propto\frac{1}{R}$