Question

The core of a toroid having `3000turns` has inner and outer radii of `11cm` and `12cm` respectively. The magnetic field in the core for a current of `0*70A` is `2*5T`. Calculate relative permeability of the core?

Answer 1

Here, `N=3000, r_1=11cm`.
`r_2=12cm, I=0*70A, B=2*5T, mu_r=?`
Mean radius `=(r_1+r_2)/(2)=(11+12)/(2)=11*5cm`
`=11*5xx10^-2m`
Number of turns per unit length,
`n=(N)/(2pir)=(3000)/(2xx3*14xx11*5xx10^-2)`
As `B=munI`
`:. mu=(B)/(nI)=(2*5xx2xx3*14xx11*5xx10^-2)/(3000xx0*7)`
`=8*6xx10^-4`
`mu_r=mu/mu_0=(8*6xx10^-4)/(4pixx10^-7)=684*4`