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A toroid core has inner radius of $0.24 \mathrm{~m}$ and outer radius of $0.26 \mathrm{~m}$. A current of 10 A flows through the wire having 2500 turns around it. Find the magnetic field inside the core of the toroid.
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Verified Answer
The correct answer is:
$2 \times 10^{-2} \mathrm{~T}$
We have
$\mathrm{r}_{\mathrm{m}}=\frac{0.24+0.26}{2}=0.25 \mathrm{~m}$
As $B=\mu_0 n I$
$\begin{aligned}
& =\frac{\mu_0 \mathrm{NI}}{2 \pi \mathrm{r}_{\mathrm{m}}} \quad\left[\because \ell=2 \pi \mathrm{r}_{\mathrm{m}}\right] \\
& =\frac{2 \times 10^{-7} \times 2500 \times 10}{0.25}=2 \times 10^{-2} \mathrm{~T}
\end{aligned}$
$\mathrm{r}_{\mathrm{m}}=\frac{0.24+0.26}{2}=0.25 \mathrm{~m}$
As $B=\mu_0 n I$
$\begin{aligned}
& =\frac{\mu_0 \mathrm{NI}}{2 \pi \mathrm{r}_{\mathrm{m}}} \quad\left[\because \ell=2 \pi \mathrm{r}_{\mathrm{m}}\right] \\
& =\frac{2 \times 10^{-7} \times 2500 \times 10}{0.25}=2 \times 10^{-2} \mathrm{~T}
\end{aligned}$
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