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Two concentric coils of 10 turns each are placed in the same plane. Their radii are $20 \mathrm{~cm}$ and $40 \mathrm{~cm}$ and carry 0.2 and $0.3 \mathrm{~A}$. current respectively in opposite directions. The magnetic induction (in T) at the centre is
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Verified Answer
The correct answer is:
$\frac{5}{4} \mu_0$
Two coils carry currents in opposite directions, hence net magnetic field at centre will be difference of the two fields. ie,
$$
\begin{aligned}
B_{\text {net }} & =\frac{\mu_0}{4 \pi} \cdot 2 \pi N\left[\frac{i_1}{r_1}-\frac{i_2}{r_2}\right] \\
& =\frac{10 \mu_0}{2}\left[\frac{0.2}{0.2}-\frac{0.3}{0.4}\right] \\
& =\frac{5}{4} \mu_0
\end{aligned}
$$
$$
\begin{aligned}
B_{\text {net }} & =\frac{\mu_0}{4 \pi} \cdot 2 \pi N\left[\frac{i_1}{r_1}-\frac{i_2}{r_2}\right] \\
& =\frac{10 \mu_0}{2}\left[\frac{0.2}{0.2}-\frac{0.3}{0.4}\right] \\
& =\frac{5}{4} \mu_0
\end{aligned}
$$
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