A long solenoid has 200 turns per cm and carriers a currenti. The magnetic field at its centre is \(6.28 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2\). Another long solenoid has 100 turns per \(\mathrm{cm}\) and it carries a current \(\frac{i}{3}\). The value of magnetic field at its centre is nearly

Magnetic field due to a long solenoid is given by
\(B=\mu_0 n i\)
For solenoid with 200 turns per \(\mathrm{cm}\) and \(i\) current flows through it,
\(6.28 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2=\mu_0 \times 200 \times i\)

Now, for solenoid with 100 turns per cm with current \(\frac{i}{3}\),
\(B=\mu_0 \times 100 \times\left(\frac{i}{3}\right)\)
Introducing value of \(i\) from equation (1),
\(B=\mu_0 \times 100 \times\left(\frac{1}{3} \times \frac{6.28 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2}{\mu_0 \times 200}\right)\) \(=1.46 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2\)
\(B \approx 1.05 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2\)