Question

Two toroids $\text{A}$ and $\text{B}$ have the total number of turns $3n$ and $n$ respectively with average radii $r$ and $3r$ respectively. If the both toroids carries equal amounts of current, the ratio of magnetic field inside the core of toroids is

• A. $1:1$
• B. $3:1$
• C. $9:1$
• D. $1:3$

Answer 1

The correct option is C $9:1$

Magnetic field produced by toroid inside the core of toroid is given by

$B=\frac{{\mu }_{0}Ni}{2\pi r}$

So for toroid $\text{A}:$

$B_A=\frac{{\mu }_0{N}_{A}i}{2\pi r_A}=\frac{3{\mu }_{0}ni}{2\pi r}$

And for toroid $\text{B}:$

$B_B=\frac{{\mu }_0{N}_{B}i}{2\pi r_B}=\frac{{\mu }_{0}ni}{6\pi r}$

$\therefore B_A:B_B=\frac{3{\mu }_{0}ni}{2\pi r}:\frac{{\mu }_{0}ni}{6\pi r}=9:1$

Hence, option $\left(c\right)$ is correct.