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Two concentric coils of 20 turns each are placed in same plane. Their radii are $30 \mathrm{~cm}$ and $60 \mathrm{~cm}$ and carry $0.4 \mathrm{~A}$ and $0.6 \mathrm{~A}$ currents respectively in opposite directions. The magnetic induction at the centre in tesla is ....... .
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Verified Answer
The correct answer is:
$\frac{10}{3} \mu_0$
As $\quad B_{\text {centre }}=\frac{\mu_0 n I}{2 r}$
So, Magnetic field at $\mathrm{O}$,
$$
\begin{aligned}
& B_O=\frac{\mu_0}{2}\left[\frac{n_1 I_1}{r_1}-\frac{n_2 I_2}{r_2}\right] \\
& n_1=n_2=20 \\
& B_O=\frac{\mu_0}{4 \pi} \cdot 2 \pi \times 20\left[\frac{0.4}{30 \times 10^{-2}}-\frac{0.6}{60 \times 10^{-2}}\right] \\
& =\frac{\mu_0}{2} \times 20\left[\frac{0.8-0.6}{60 \times 10^{-2}}\right]=\frac{10}{3} \mu_0
\end{aligned}
$$
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