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A solenoid $2 \mathrm{~m}$ long and $4 \mathrm{~cm}$ in diameter has 4 layers of windings of 1000 turns each and carries a current of $5 \mathrm{~A}$. what is the magnetic field at its centre along the axis?
$\left[\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\right]$
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$\left[\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\right]$
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Verified Answer
The correct answer is:
$4 \pi \times 10^{-3} \mathrm{~T}$
$\begin{aligned} & \mathrm{B}=\mu_0 \mathrm{nI} \\ & \mathrm{n}=\frac{\mathrm{N}}{\mathrm{L}}=\frac{4 \times 1000}{2}=2000 \text { turns } / \mathrm{m}, \mathrm{I}=5 \mathrm{~A} \\ & \therefore \mathrm{B}=4 \pi \times 10^{-7} \times 2000 \times 5 \\ & =4 \pi \times 10^{-3} \mathrm{~T}\end{aligned}$
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