Question

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

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

Answer 1

Answer: (C)

We have $B =\frac{\mu_{0} \mu_{r} N_{i}}{2 \pi r}$
$1 =\frac{4 \pi \times 10^{-7} \times \mu_{r} \times 400 \times 2}{2 \pi \times 40 \times 10^{-2}}$
$\mu_{r} =\frac{2 \pi \times 400 \times 10^{-2}}{4 \pi \times 10^{-7} \times 800}= \frac{80 \times 10^{-2}}{4 \times 10^{-7} \times 800}$
$=\frac{80 \times 10^{5}}{4 \times 800}=2500$