Question

A toroid with mean radius $r_0$ and diameter $2a$ has N turns carrying current I. What is the magnetic field B inside the toroid?

• A. $\frac{{\mu }_{0}NI}{{2\pi r}_0}$
• B. $\frac{{\mu }_{0}NI}{{2\pi (r}_0+a)}$
• C. $\frac{{\mu }_{0}NI}{{\pi (r}_0+a)}$
• D. Zero

Answer 1

The correct option is A $\frac{{\mu }_{0}NI}{{2\pi r}_0}$

Along path 2, inside the toroid, we apply Ampere's Law
$\int B.dl={\mu }_o{i}_{enc}$

$B\times 2\pi r_0={\mu }_o\times NI$

$B=\frac{{\mu }_{o}NI}{2\pi r_0}$