Question

A toroidal solenoid is given which has inner and outer radii as $28cm$ and $29cm$ respectively. If it is constructed with $3700$ turns of wire around the core and a current of $10A$ flows in it, then calculate the magnetic field inside the core of the toroid.

• 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 $n=\frac{N}{2 \pi r_{a v}}$
The average radius of toroid
$r_{a v}=28.8 \, cm=28.5\times 10^{- 2} \, m$
$\therefore \, n=\frac{3700}{2 \times 3.14 \times 28.5 \times 10^{- 2}}=2067.27\approx2067$
Now, $B=\mu _{o}nI=4\pi \times 10^{- 7}\times 2067\times 10$
$=259615.2\times 10^{- 7} \, T=2.60\times 10^{- 2} \, T$