Question

The current in the windings on a toroid is 2 A. There are 400 turns and the mean radius is 40 cm. If the magnetic field inside is 1 T, the relative permeability is :

• A. 200
• B. 250
• C. 400
• D. 150

Answer 1

The correct option is B 250

Given,

$B=1T$

$i=2A$

$r=40cm=0.4m$

$N=400turn$

The magnetic field due to toroid is given by

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

${\mu }_r=\frac{2\pi rB}{{\mu }_{0}Ni}$

${\mu }_r=\frac{2\times 3.14\times 0.4\times 1}{4\times 3.14\times {10}^{-7}\times 400\times 2}$

${\mu }_r=\frac{2512000}{10048}$

${\mu }_r=250$