A toroid is a hollow non-conducting circular ring, on which a large number of turns of a conducting…

A toroid is a hollow non-conducting circular ring, on which a large number of turns of a conducting wire are closely wound. If a solenoid is bent into a circular shape and the ends are joined, we get a toroid. Consider a toroid having centre O, number of turns N and each carrying a current I. By Ampere's law, in the case of a toroid: STEP 1: $\oint B \cdot dl = \mu_0\text{ (Total current)} = \mu_0$ ____ $I$ (Rewrite STEP 1 and fill in the blank with an appropriate substitution) STEP 2: $B$ ____ $= \mu_0 NI$ (Rewrite STEP 2 and fill in the blank with an appropriate substitution) $\therefore B = \frac{\mu_0 NI}{2\pi r} = \mu_0 I \left[\frac{N}{2\pi r}\right]$ If n is the number of turns per unit length, then $n = \frac{N}{2\pi r}$ STEP 3: $B = \mu_0$ ____ $I$ (Rewrite STEP 3 and fill in the blank with an appropriate substitution)