A long solenoid has $200$ $turns$ per $cm$ and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2} $ $\frac{{Wb}}{{{m^2}}}$ Another long solenoid has $100$ $turns$ per $cm$ and it carries a current $\frac{I}{3}\;$ . The value of the magnetic field at its centre is
AIEEE 2006, Medium
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$\frac{B_{2}}{B_{1}}=\frac{\mu_{0} n_{2} i_{2}}{\mu_{0} n_{1} i_{1}} \Rightarrow \frac{B_{2}}{6.28 \times 10^{-2}}=\frac{100 \times \frac{i}{3}}{200 \times i}$
$\Rightarrow B_{2}=\frac{6.28 \times 10^{-2}}{6}=1.05 \times 10^{-2} \,\mathrm{Wb} / \mathrm{m}^{2}$
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