Question

The magnetic field inside the coils of a toroid of radius $R$ and $N$ turns with a current of $IA$ is given by

• A. $B=\frac{{\mu }_{o}NI}{4\pi R}$
• B. $B=\frac{{\mu }_{o}NI}{2\pi R}$
• C. $B={\mu }_{o}NI$
• D. None of these

Answer 1

The correct option is B $B=\frac{{\mu }_{o}NI}{2\pi R}$

Let radius of toroid = r

Current = I

Number of turns = N

Magnetic field =?

Using Ampere's circuital law

$\int \overrightarrow{B}.\overrightarrow{d}l={\mu }_0{I}_c$

$⟹B.2\pi r={\mu }_{0}NI$

$⟹B=\frac{{\mu }_{0}NI}{2\pi r}$