Question

The current in the winding on a toroid is $2.0A$. There are $400$ turns and the mean circumferential length is $40cm$. If the inside magnetic field is $1.0T$, the relative permeability is near to

• A. 1000
• B. 2000
• C. 2500
• D. 4000

Answer 1

Answer: (C)

We have $B=\frac{{\mu }_0{\mu }_r{N}_i}{2\pi r}$
$1=\frac{4\pi \times 10^{-7}\times {\mu }_r\times 400\times 2}{2\pi \times 40\times 10^{-2}}$
${\mu }_r=\frac{2\pi \times 400\times 10^{-2}}{4\pi \times 10^{-7}\times 800}=\frac{80\times 10^{-2}}{4\times 10^{-7}\times 800}$
$=\frac{80\times 10^5}{4\times 800}=2500$