Question

The inner and outer radius of a toroid core are $28 \,cm$ and $29\, cm$ respectively and around the core $3700$ turns of a wire are wounded. If the current in the wire is $10\, A$, then the magnetic field inside the core of the toroid is

• A. $2.60 \times 10^{-2}\, T$
• B. $2.60 \times 10^{-3}\, T$
• C. $4.52 \times 10^{-2}\, T$
• D. $4.52 \times 10^{-3}\, T$

Answer 1

Answer: (A)

The number of turns per unit length for the given toroid $n=\frac{N}{2\pi r_{av}}$
The average radius of toroid
$r_{av}=\frac{28+29}{2}=28.5\,cm$
$=28.5\times10^{-2}\,m$
$\therefore n=\frac{3700}{2\times3.14\times28.5\times10^{-2}}$
$=2067.27 \approx2067$
Now, $B=\mu_{0}nI=4\pi\times10^{-7}\times2067\times10$
$=259615.2\times10^{-7}\, T $
$=2.60\times10^{-2}\, T$