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A coil wrapped around a toroid has inner radius $10.0 \mathrm{~cm}$ and an outer radius of $30.0 \mathrm{~cm}.$ If the coil is wrapped makes $1000$ turns and carnies current of $$6 A$,$ find the magnetic field (a) Inside the cone of the toroid $?$
Option: 1
$0.0048T$

Option: 2
$0.0046T$

Option: 3
$0.0025T$

Option: 4
$0.0024T$

Answers (1)

best_answer

Here,

$\begin{aligned} & \eta_{\text {inner }}=20.0 \mathrm{~cm} \quad I=6 \mathrm{~A} \\ & n_{\text {outer }}=30.0 \mathrm{~cm} \\ & \end{aligned}$

$\begin{aligned} \text { Mean } \Rightarrow n=\frac{20+30}{2}=\frac{50}{2} & =2.5 \mathrm{em} \\ & =25 \times 10^{-2} \mathrm{~m} \end{aligned}$

Total length of the tonoid $=$ circumference of the tonoid

$\begin{aligned} & =2 \pi n \\ & =2 \pi \times 0.25 \\ & =0.50 \pi \mathrm{m} \end{aligned}$

Total number of turns, $N=1000$

Number of turns per unit length

$n=\frac{N}{2 \pi n}=\frac{1000}{0.50 \pi} m^{-1}$

$B=\mu_0 n I=\left(4 \times \pi \times 10^{-7}\right) \times \frac{1000}{0.50 \pi \times} \times 6=0.0048T$

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Gaurav

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