Q140 / 150 · MHT CET 2024 (03 May Shift 1) · Physics

A current of 5 A flows through a toroid having a core of mean radius 20 cm . If 4000 turns of the conducting wire are wound on the core, then the magnetic field inside the core of the toroid is [permeability of free space $=4 \pi \times 10^{-7}$ SI units]

  • A
    $8 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2$
  • B
    $6 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2$
  • C
    $5 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2$
  • Correct answer
    D
    $\quad 2 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2$

Solution

$\begin{aligned} \mathrm{B} & =\frac{\mu_0 \mathrm{nI}}{2 \pi \mathrm{r}}=\frac{4 \pi \times 10^{-7} \times 4000 \times 5}{2 \pi \times\left(20 \times 10^{-2}\right)}=\frac{1}{50} \\ & =2 \times 10^{-2} \mathrm{wb} / \mathrm{m}^2\end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions