A solenoid $2 \mathrm{~m}$ long and $4 \mathrm{~cm}$ in diameter has 4 layers of windings of 1000 turns each…

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? $\left[\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\right]$
  1. $10^{-3} \mathrm{~T}$
  2. $2 \pi \times 10^{-3} \mathrm{~T}$
  3. $4 \pi \times 10^{-3} \mathrm{~T}$
  4. $8 \pi \times 10^{-3} \mathrm{~T}$

Solution

$\begin{aligned} & \mathrm{B}=\mu_0 \mathrm{nI} \\ & \mathrm{n}=\frac{\mathrm{N}}{\mathrm{L}}=\frac{4 \times 1000}{2}=2000 \text { turns } / \mathrm{m}, \mathrm{I}=5 \mathrm{~A} \\ & \therefore \mathrm{B}=4 \pi \times 10^{-7} \times 2000 \times 5 \\ & =4 \pi \times 10^{-3} \mathrm{~T}\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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