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A solenoid is 1.5 m long and its inner diameter is 4.0 cm. It has three layers of windings of 1000 turns each and carries a current of 2.0 A. The magnetic flux through a cross-section of the solenoid is nearly

1. 2.5 × 10^-7 weber
2. 6.31 × 10^-6 weber
3. 5.2 × 10^-5 weber
4. 4.1 × 10^-5 weber

Correct answer: 6.31 × 10^-6 weber

Solution

Inside a long solenoid, $B=\mu_0 n I$, where $n$ is turns per unit length. Here total turns $N=3000$, so $n=3000/1.5=2000\,\text{m}^{-1}$ and $B=4\pi\times10^{-7}\times2000\times2$. The cross-sectional area is $\pi(0.02)^2$, giving flux $\Phi=BA\approx6.31\times10^{-6}\,\text{Wb}$.

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