Question

The core of a toroid having $3000$ turns has inner and outer radial $11\text{cm}$ and $12\text{cm}$ respectively. The magnetic field in the core for a current of $0.7\text{A}$ is $2.5\text{T}$. Calculate the relative permeability of the core ?

• A. $684$
• B. $290$
• C. $395$
• D. $768$

Answer 1

The correct option is A $684$

Given:
$N=3000;r_1=11\text{cm};r_2=12\text{cm}$
$i=0.7\text{A}$ and $B=2.5\text{T}$

So the mean radius of toroid will be

$r=\frac{r_1+r_2}{2}=11.5\text{cm}=11.5\times {10}^{-2}\text{m}$

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

$B=\frac{{\mu }_0{\mu }_{r}Ni}{2\pi r}$

$2.5=\frac{4\pi \times {10}^{-7}\times {\mu }_r\times 3000\times 0.7}{2\pi \times 11.5\times {10}^{-2}}$

${\mu }_r=\frac{2.5\times 2\pi \times 11.5\times {10}^{-2}}{4\pi \times {10}^{-7}\times 3000\times 0.7}$

$\therefore {\mu }_r\approx 684$

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

Why this question ? Concept : Magnetic field, $B=\mu ni$ Here, $\mu ={\mu }_0{\mu }_r$